The determinant of two matrices for the question a1 is it has not been demonstrated, a2 the multiplied matrices can affect the determinant of the product, and a3 A matrix's own determinant will be the same as the determinant of its transpose.
a1.) Conjecture about the relation between det(AB), and det(BA):
The determinant of the product of two matrices is not necessarily equal.
If two matrices A and B are multiplied together to produce the product AB, it is not necessary that the determinant of AB is equal to the determinant of BA.
This is a conjecture that has not yet been demonstrated in every case.%
a2.) Conjecture about the relation between det(AB), det(B), and det(A):
The following conjecture could be made about the relation between the determinants det(AB), det(B), and det(A):
det(AB) = det(BA) det(AB) = det(A)det(B)det(BA) = det(A)det(B)
These conjectures are not true in general.
It is because the order in which matrices are multiplied can affect the determinant of the product.%
a3.) Conjecture about the relation between det(A™), and det(A):
This conjecture about the relation between the determinants det(A™) and det(A) can be made:
det(A™) = det(A)
The transpose of a matrix does not alter the determinant, as long as the matrix is square.
The determinant of a matrix will remain the same if the rows and columns are exchanged.
Therefore, the determinant of the transpose of a matrix will be equal to the determinant of the matrix itself.
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The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?
7/19 as a percentage, round your answer to the nearest tenth of a percent
Answer: 36.8
Step-by-step explanation:
First convert 7/19 to a decimal.
7/19 = 0.368421...
Then to convert a decimal a percent by multiplying by 100
0.3684... x 100 = 36.8
Mr hawkins is covering a wall with wallpaper the wall measures 11 feet by 15 feet each square foot costs 3. 10 find the cost of covering the wall with wall paper
The cost of covering the wall with wall paper is 495.
the lengthe of the wall = 11 feet
the width of the wall = 15 feet
so, the area of the wall
A = the length of the wall x the width of the wall
A = 11 x15
A = 165 square foot
then, the total cost is
= 165 x 3
= 495
So, the cost of covering the wall with wall paper is 495.
The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x time y.
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in triangle abc, the length of side ab is 16 inches and the length of side bc is 24 inches. which of the following could be the length of side ac?
We have triangle ABC, the length of side AB is 16 inches and the length of side BC is 24 inches, the possible length of the side AC is less than 40 inches
To find the possible length of side AC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side, that is, a + b > c, b + c > a, c + a > b.
Now, for the given triangle ABC:
a = AB = 16 inches
b = BC = 24 inches
c = AC
We know that a + b > c (using the triangle inequality theorem)
16 + 24 > cc < 40
Therefore, By using the triangle inequality theorem, the possible length of the side AC is less than 40 inches.
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how do i work this out i dont understand it
Answer:
37
Step-by-step explanation:
we know that:
C=?
c=17
b=26
a=14
using the law of cosine:
[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]
[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]
Samuel bought four adult tickets to a movie for $48. Erica bought 3 adult tickets to a movie at a different theater. Erica paid $2.50 more than Samuel for each movie ticket she bought. How much did Erica spend on her movie ticket purchase?
Answer: £43.50
Step-by-step explanation:
each ticket from samuel is £12 if erica is spending £2.50 more per ticket that is £14.50 per ticket. £14.50 x 3 = £43.50
URGENT :
In a shot put event, an athlete throws the shot put from an initial height of 6 feet and with an initial vertical velocity of 29 feet per second. How long until it reaches the ground?
equation is h=-16t^2+29t+6
Check the picture below.
so if we just set h = 0, we'll get the "t" when that happened
[tex]\stackrel{h}{0}=-16t^2+29t+6\implies 0=-(16t^2-29t-6)\implies 0= 16t^2-29t-6 \\\\\\ 0=(t-2)(16t+3)\implies t= \begin{cases} ~~ ~ 2 ~~ \checkmark\\ -\frac{3}{16} ~~ \bigotimes \end{cases}[/tex]
now, let's notice that we get two valid values for "t", however the negative doesn't apply in this case, because we can't quite have negative seconds for the object in motion.
Answer:
2
Step-by-step explanation:
h(t) = -16t² + 29t + 6
h(2) = -16 * 2² + 29 * 2 + 6
h(2) = 0
t = 2 second's
Write this value in order , starting with the smallest 0. 2 1/2 2℅
0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.
0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.
2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.
2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.
Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.
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Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answer:
Step-by-step explanation:
Find an explicit formula for the arithmetic sequence 12, 5, -2, -9,. 12,5,−2,−9,. 12, comma, 5, comma, minus, 2, comma, minus, 9, comma, point, point, point Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text. A(n)=
The explicit formula for the arithmetic sequence 12, 5, -2, -9,..is a(n) = -7n + 19.
To find the explicit formula for this arithmetic sequence, we first need to determine the common difference, which is the amount by which each term differs from the previous term.
d = 5 - 12 = -7
d = -2 - 5 = -7
d = -9 - (-2) = -7
Since the common difference is -7, we can use the formula for an arithmetic sequence:
a(n) = a (1) + (n - 1) d
where a(n) is the nth term of the sequence, a (1) is the first term, n is the term number, and d is the common difference.
Plugging in the given values, we get:
a(n) = 12 + (n - 1) (-7)
Simplifying, we get:
a(n) = -7n + 19
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The explicit formula for the arithmetic sequence will be f(n) = 19 -7n.
f(n) = a + (n - 1) d,
where an is the first term and is the explicit formula for an arithmetic series.
d = Common Difference
n = number of terms
The provided arithmetic series is = 12, 5, -2, -9.
First term: a = 12.
Common variation: d= 5-12= 7
[Difference between any two words that follow one another.]
When a = 12 and d = -7 are entered into equation (1), we obtain
f(n) = 12 + (n - 1) ( - 7 )
Thus, the explicit formula for the above arithmetic sequence is
f(n) = 12 = (n - 1). ( - 7 )
If we continue to solve it, we obtain
f(n) = 12 - 7n + 7
f(n) = 19 - 7n
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The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.
a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
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AREA/ PERIMETER/ VOLUME
Find the perimeter and area.
12m
10m
9m
8m
Step-by-step explanation:
Perimeter:
12m + 10m + 8m + (10 - 8)m + 9m + (12 - 9)m = 44m
or
12m * 2 + 10m * 2 = 44m
Area:
A = 9m * 8m + 12m * (10 - 8)m
A = 72m² + 24m² = 96m²
Find the circumference of a circle with diameter, d = 1.26m.
Give your answer rounded to 2 DP
Answer: b
Step-by-step explanation: just took it on edge.
Suppose that 6 out of the 19 doctors in a small hospital are General Practitioners, 5 out of the 19 are under the age of 40 , and 2 are both General Practitioners and under the age of 40. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 40
The probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 from a small hospital is 9/19, given 6 out of 19 are General Practitioners, 5 out of 19 are under 40, and 2 are both.
To find the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40, we need to add the probabilities of these two events and subtract the probability of selecting a doctor who is both a General Practitioner and under the age of 40, since we don't want to count that case twice:
P(General Practitioner or under 40) = P(General Practitioner) + P(Under 40) - P(General Practitioner and under 40)
we know 6 out of 19 doctors are General Practitioners, 5 out of 19 doctors are under the age of 40, 2 doctors are both General Practitioners and under the age of 40.
Therefore:
P(General Practitioner) = 6/19
P(Under 40) = 5/19
P(General Practitioner and under 40) = 2/19
Substituting these values into the formula:
P(General Practitioner or under 40) = 6/19 + 5/19 - 2/19
= 9/19
Therefore, the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 is 9/19.
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The numbers of trading cards owned by 7 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
360, 373, 402, 499, 548, 644, 646
Suppose that the number 646 from this list changes to 639. Answer the following.
a) If the number 646 from the ordered list changes to 639, c) the median stays the same.
b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.
What are the median and the mean?The median is the middle value in an ordered list (descending or ascending).
The mean refers to the average value.
The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.
The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646
The total value (sum) = 3,472
The number of cards = 7
The median = 499
The mean = 496 (3,472/7)
If the number 646 changes too 639:
The total value (sum) = 3,465
The median = 499
The mean = 495 (3,465/7)
Difference in mean = 1 (496 - 495)
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Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is shorter and more spread out than curve Upper B, and curve Upper B is farther to the right than curve Upper A.
Select all that apply:
1. A has the larger mean.
2. B has the larger mean.
3. The means of A and B are equal.
4. A has the larger standard deviation.
5. B has the larger standard deviation.
6. The standard deviations of A and B are equal
Answer:
False
True
False
True
False
False
Step-by-step explanation:
From the plot, we can see that curve B is taller and more narrow than curve A, and it is shifted to the right relative to curve A. This tells us that curve B has a larger mean and smaller standard deviation than curve A. Therefore, statement 2 is true, and statements 1, 3, 5, and 6 are false. Finally, since curve A is more spread out than curve B, it has a larger standard deviation. Therefore, statement 4 is true.
a display shelf in a retail shop will showcase the stores handmade artisan soaps. the length of the shelf given to each bar of soap will be uniformly distributed with a mean of 3 inches and a standard deviation of 0.5 inch. for 50 bars of soap what is the probability the length of the display will exceed 154 inches?
The probability the length of the display will exceed 154 inches is 0.1292
What is the probability?The probability that the length of the display shelf given to each bar of soap will exceed 154 inches when there are 50 bars of soap is 0.0062 or 0.62%. This is because the mean is 3 inches and the standard deviation is 0.5 inches, which means that the length of the display will have a normal distribution.
We can calculate this probability by using the following formula:
P(x > 154) = P (x > 154 - 50 × 3/√(50×0.5)) = P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.870 = 0.1292
The probability the length of the display will exceed 154 inches is 0.1292.
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some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the equivalent closed form for the original rate function is
.[tex]S π/t 4tan (t) dt = -4 ln |cos (t)| + C.[/tex]
a. [tex]S π / π /4 5t+4 / t² + 1 dt[/tex]We can write this rate function as a sum of two functions by expanding the denominator:
[tex]S π / π /4 5t+4 / (t² + 1) dt = S π / π /4 5t+4 / (t² + 1) (t+1/t - 1/t) dt = S π / π /4 5t+4 (t+1 - 1/t²) dt = S π / π /4 5t+4 (t+1) dt - S π / π /4 5t+4 (1/t²) dt[/tex]
Now, integrating the two functions gives us the closed form:
[tex]S π / π /4 5t+4 (t+1) dt = 5/2 (t² + 2t + 2) + CS π / π /4 5t+4 (1/t²) dt = -5/2 (t + 1/t) + C[/tex]
Therefore, the equivalent closed form for the original rate function isS π / π /4 5t+4 / t² + 1 dt = 5/2 (t² + 2t + 2) - 5/2 (t + 1/t) + C.
b. S π/t 4tan (t) dt
We can use a trig identity to change the form of this rate function:
S π/t 4tan (t) dt = S π/t 4 (sin (t) / cos (t)) dt = 4/cos (t) S π/t sin (t) dt
Integrating the rate function gives us the closed form:
S π/t 4tan (t) dt = 4/cos (t) S π/t sin (t) dt = -4 ln |cos (t)| + C.
Therefore, the equivalent closed form for the original rate function is:
S π/t 4tan (t) dt = -4 ln |cos (t)| + C.
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3
The ratio of desktop computers to laptop computers sold by
a mail-order company last week was 8 to 3. What could be
the numbers of computers sold by the company last week?
A
B
C
D
448 desktops, 168 laptops
448 desktops, 165 laptops
440 desktops, 168 laptops
400 desktops, 165 laptops
using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.
How to Calculate Ratios?To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.
Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:
A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168
B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165
C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168
D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165
Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.
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find the number of ways of arranging the numbers ${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$ in a row so that the product of any two adjacent numbers is even.
Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.
What are the fundamental products?Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.
We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.
Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.
Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.
Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.
Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.
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An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis
The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.
The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.
The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.
According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.
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A spherical balloon is inflated so that it’s radius (r) increases at a rate of 2/r cm/sec. How fast is the volume of the balloon increasing when the radius is 4 cm?
Answer:
32π cm³/sec
Step-by-step explanation:
List given information
[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\r=4\\\\\frac{dr}{dt}=\frac{2}{r}\\ \\\frac{dV}{dt}=\,\,?[/tex]
Solve for dV/dt
[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{dr}{dt}\biggr)\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{2}{r} \biggr)\\\\\frac{dV}{dt}=4\pi (4)^2\biggr(\frac{2}{4} \biggr)\\\\\frac{dV}{dt}=4\pi(16)\biggr(\frac{1}{2} \biggr)\\\\\frac{dV}{dt}=4\pi(8)\\\\\frac{dV}{dt}=32\pi[/tex]
Hence, the volume of the balloon is increasing at a rate of 32π cm³/sec when the radius is 4 cm.
A box contains 4 bags of sugar. The mass of each bag is 6 kilograms. What is the total mass of the box in grams?
240,000 grams
24,000 grams
2,400 grams
240 grams
Answer: 24000 g
Step-by-step explanation:
multiply together:
4 bags * 6 kg = 24 kg total
convert:
1 kg = 1000 g
24 kg * (1000 g / 1 kg) = 24000 g
To calculate the total mass of the box in grams, we need to first calculate the total mass of the 4 bags of sugar in kilograms, and then convert that to grams.
The mass of one bag of sugar is 6 kilograms.
The total mass of all 4 bags is:
4 bags x 6 kilograms/bag = 24 kilograms
To convert 24 kilograms to grams, we multiply by the conversion factor of 1000 grams/kilogram:
24 kilograms x 1000 grams/kilogram = 24,000 grams
Therefore, the total mass of the box, including all 4 bags of sugar, is 24,000 grams.
The correct answer is B) 24,000 grams.
A cat gave birth to 333 kittens who each had a different mass between 147147147 and 159\,\text{g}159g159, start text, g, end text. Then, the cat gave birth to a 4^{\text{th}}4 th 4, start superscript, start text, t, h, end text, end superscript kitten with a mass of 57\,\text{g}57g57, start text, g, end text.
The answer to the question is 334 kittens.
Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.
First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g
Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.
Therefore, the answer to the question is 334 kittens.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 3)
The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
How to use Pythagoras theorem to find distance?To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.
We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]
Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
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Draw a model to show that 3=6/2 explain your drawing
Equivalent fractions are defined as fractions that are equal to the same value, regardless of their numerators and denominators.
Equivalent fractions can be defined as fractions that may have different numerators and denominators but represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both simplify to 3/4. 1/2, 2/4, 3/6 and 4/8 are equivalent fractions. Let's see how their values are equal. We will represent each of these fractions with a shaded circle.
It can be seen that, seen as a whole, the hatched parts in all the figures represent the same parts.
Equivalent fractions can be written by multiplying or dividing the numerator and denominator by the same number. This is why these fractions reduce to the same number when they are simplified.
Multiply the numerator and denominator by the same number.Numerator and denominator divide by the same number.Learn more about Fraction:
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Under certain conditions, sound can travel 768 miles per hour. Under these conditions, Alan hears thunder 45 seconds after seeing lightening. His friend, Ryan hears thunder after seeing the same lightening in 30 seconds. What is the longest and the shortest possible distance that Alan and his friend are apart.
The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.
What is sound?Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.
In the given question,
Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:
d/768 = 45 - 30 = 15
Solving for d, we get:
d = 15 x 768 = 11520
So the distance between Alan and Ryan is 11520 miles.
If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:
d/750 = 15
d = 15 x 750 = 11250
Therefore, the minimum distance between Alan and Ryan is 11250 miles.
If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:
d/800 = 15
d = 15 x 800 = 12000
Therefore, the maximum distance between Alan and Ryan is 12000 miles.
Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.
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jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
what is proportionality ?A mathematical relationship called proportionality asserts that two values are related in such a way that if one quantity rises or falls, the other quantity rises or falls by a fixed amount. The proportionality constant, also known as this constant factor, is typically represented by the letter "k".
given
The remaining 70% of Jerome's 1,040 songs are not country songs if only 30% of them are.
We can use the following calculation to get the proportion of non-country songs:
70% of 1,040 = 0.7 x 1,040 = 728
As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
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How to find the missing side of a triangle using the Law of Sines?
Step-by-step explanation:
the law of sine is
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides. A, B, C are the corresponding opposing angles.
you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.
Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2