Answer:
S₄₀ = 2780
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
14 - 11 = 17 - 14 = 3
this indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 11 and d = 3 , then
S₄₀ = [tex]\frac{40}{2}[/tex] [ (2 × 11) + (39 × 3) ]
= 20( 22 + 117)
= 20 × 139
= 2780
Omar owns a small business selling ice-cream. He knows that in the last week 32
customers paid cash, 2 customers used a debit card, and 26 customers used a credit
card.
a
a
If next week, he is expecting 1500 customers, about how many would you expect to
pay with a debit card? Round your answer to the nearest whole number.
a
The number of customers who will pay by debit card will be 50.
What are fractions?The fraction is defined as the division of the whole part into an equal number of parts.
Last week there were
32 + 2 + 26 = 60 customers.
That means that the fraction of the customers, who paid by debit card, was
2/60 = 1/30
In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.
we simply say that we expect the same fraction, 1/30 if customers use credit cards.
for the absolute number of predicted debit card customers we multiply the predicted number of customers by the expected fraction
1500 × 1 / 30 = 1500 / 30 = 50
Therefore the number of customers who will pay by debit card will be 50.
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calculate the value of the marked angle
(4, 6) (-3, -2) Find the slope
Answer:
The value of the slope would be:
8/7
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Answer:
[tex] slope = \dfrac{8}{7} [/tex]
Step-by-step explanation:
(4, 6) and (-3, -2)
[tex] slope = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = \dfrac{-2 - 6}{-3 - 4} [/tex]
[tex] slope = \dfrac{-8}{-7} [/tex]
[tex] slope = \dfrac{8}{7} [/tex]
Lethna buys some boxes of pens and some packets of pencils.
There are 40 pens in each box. There are 12 pencils in each packet.
Lethna gives one pen and one pencil to each student in Year 7 of her school.
When she has done this she has no pens left and no pencils left.
Work out how many boxes of pens and how many packets of pencils Lethna could
have bought
Answer:
pen: 3 boxes [pencils : 10 packets
Step-by-step explanation:
40 and 12 4|40/10 12/3 4x3x10=120
pen 120 divided by 40 = 3 boxes
pencils 120 divided by 12 = 10 packets
We want to find the zeros of this polynomial:
p(x) = (x+2) (2x^2 + 3x-9)
Answer:
x = - 2, x = - 3, x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
to find the zeros equate p(x) to zero , then
(x + 2)(2x² + 3x - 9) = 0 ← factor the quadratic
(x + 2)(x + 3)(2x - 3) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 3 = 0 ⇒ x = - 3
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
Select the correct answer.
Tracy wants to make a cylindrical model. The height of the cylindrical model, H(V), in inches, is modeled by this
equation, where Vis the volume of the cylindrical model, in cubic inches.
H(V) = 2. 6937
What is the average rate of change of the model's height when its volume changes from 512 cubic inches to
1,000 cubic inches?
The model's height increases by approximately 21. 52 inches for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 022 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 011 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 26. 9 inches for every 1-cubic-inch increase in its volume.
The average rate of change of the height function is slope of the height function
The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
How to determine the average rate of change?The height function is given as:
[tex]H(V) = 2.69\sqrt[3]{V}[/tex]
When V = 512, the function becomes
[tex]H(512) = 2.69\sqrt[3]{512}[/tex]
[tex]H(512) = 21.52[/tex]
Similarly;
When V = 1000, the function becomes
[tex]H(1000) = 2.69\sqrt[3]{1000}[/tex]
[tex]H(1000) = 26.9[/tex]
The average rate of change is then calculated as:
[tex]H' = \frac{H(1000) - H(512)}{1000 - 512}[/tex]
This gives
[tex]H' = \frac{26.9 - 21.52}{1000 - 512}[/tex]
[tex]H' = \frac{5.38}{488}[/tex]
Evaluate the quotient
[tex]H' = 0.01102459016[/tex]
Approximate
[tex]H' = 0.011[/tex]
Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
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Answer:
The model’s height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
Step-by-step explanation:
Plato/Edmentum
In a circle, a 225° sector has area 250pi in^2. What is the radius of the circle?
Answer:
r = 200
Step-by-step explanation:
[tex]Area of sector = (\frac{225}{360})[/tex]×πr² = [tex](\frac{5}{8})[/tex] ×πr²
[tex](\frac{5}{8})[/tex] ×πr² = 250π
[tex](\frac{5}{8})[/tex] ×r² = 250
r² = [tex](\frac{8}{5})[/tex] × 250
r² = 400
r = 200 (r is a length so, it's positive)
Pls help me!!! I need to find what b is??
Answer:
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the right angle), one angle with a measure of 30° and another with 60°
We are also given that one of the legs (one of the sides that makes up the right angle) is 5
We want to find what b is
This triangle is a special right triangle, a 30-60-90 triangle
In a 30-60-90 triangle, if the hypotenuse (the side opposite from the right angle) is b, the leg that is opposite from the 30° angle is [tex]\frac{b}{2}[/tex], while the leg that is opposite from the angle that is 60° is [tex]\frac{b\sqrt{3} }{2}[/tex]
In this case, we're given that the side opposite from the 60 degree angle is 5, meaning that 5 is equal to [tex]\frac{b\sqrt{3} }{2}[/tex]
So we can set 5 equal to [tex]\frac{b\sqrt{3} }{2}[/tex], to solve for b:
5=[tex]\frac{a\sqrt{3} }{2}[/tex]
Multiply both sides by 2
5*2=b√3
10=b√3
Now divide both sides by √3
[tex]\frac{10}{\sqrt{3} } =b[/tex]
rationalize the denominator
[tex]\frac{10 * \sqrt{3} }{\sqrt{3} *\sqrt{3} }[/tex] = b
[tex]\frac{10 \sqrt{3} }{\sqrt{9}}[/tex]= b
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
The answer can be left as that.
Hope this helps!
What is the value of sin180?
Answer:
sin180° = 0
Step-by-step explanation:
using your calculator or graph to find
sin180° = 0
Answer:
0
Step-by-step explanation:
The exact value of sin 180 is zero. Sine is one of the primary trigonometric functions which helps in determining the angle or sides of a right-angled triangle. It is also called trigonometric ratio.
What does Mean median and mode mean?
Answer:
mean-average of a data set
mode-most common number in a set
median-middle number of the set
Step-by-step explanation:
you can ask me a question for more info
Answer:
Step-by-step explanation:
Mean - Is the average taken for a set of numbers
Median - The middle value in a data set of numbers
Mode - The number that occurs the most in a given list of numbers.
Heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag, replaces it, and then draws another marble. what is p(red then blue then green)?
Multiply the probability of each by each other:
Probability of red = 1/4
Probability of blue = 1/4
Probability of green = 2/4 = 1/2
probability of red then blue then green = 1/4 x 1/4 x 1/2 = 1/32
answer: 1/32
Angle 1 and Angle _____________ are supplementary angles.
Answer: number 2
Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.
In which quadrant does θ lie given that sinθ < 0 and cosθ < 0? Thank You!
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:
Quadrant III yw :3
Step-by-step explanation:
4.5
3
5
х
Find the length of x
You use 4 gallons of water on 30 plants in your garden. At that rate, how much water
will it take to water 45 plants?
Answer:
6 gallons
Step-by-step explanation:
30-----------4
45------------x
30x = 45x4
30x=180
x=6
A shortcut:
45 is ( 30+ half of 30)
( 4 + half of 4) = 4+2 =6
6 gallons
Step-by-step explanation:[tex]Assuming\ that\ it\ will\ take\ x\ gallons\ waters[/tex]
[tex]to\ water\ 45\ plants.[/tex]
[tex]4:30=x:45[/tex]
[tex]30x=4\times 45[/tex]
[tex]30x=18[/tex]°
[tex]x=180\div 3\\ x=6[/tex]
[tex]\left\{If\right.\ a:b=c:d,\ then\ ad=\left.\ bc\right\}[/tex]
I hope this helps you
:)
(will mark brainlist)
How would we name the polyonomi ?
PLS SOMEONE HELP ME FIND THE ANSWER AND EXPLAIN #1 to me. and maybe steps. Also if you can help with any other questions that be nice! ILL MARK BRAINLIST
Answer:
I don't necessarily understand your question but usually the answer to a polynomial question is a binomial answer
Is 5.23 * 10 the 8th power in scientific notation?
Answer:
yes
Step-by-step explanation:
anything with 10^n multiplied by a number from 0 to 10 is
Hello! How to do 10 part (c)?
which features of a figuer JKLM remain the same after any rigid transformation i-ready
The rigid transformation of figure JKLM would not change the side length and angle measure
The features of the figure JKLM that would remain the same are its side lengths and angles
How to determine the features?A rigid transformation is any of the following
TranslationRotationReflectionAll of the above transformation do not change the side length and the angle measure of the shape they transform
Hence, the features of the figure JKLM that would remain the same are its side lengths and angles
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Write the y-intercept of the graph of 8x − 4y = 2?
Answer:
b= -1/2
Step-by-step explanation:
-2/4 is simplified to -1/2 as the y-intercept
y= -4x - 1/2
Find the area of the figure.
Answer: 300 ft^2
Step-by-step explanation:
First, find the area of the rectangle on the bottom:
Area of a rectangle = length * width = 18 * 12 = 216
Now, find the area of the trapezoid:
Area of a trapezoid = (base 1 + base 2) / 2 * height → (10 + 18) / 2 * 6 = 84
Add these together: 216 + 84 = 300 ft^2 :)
A sandbox has a volume of 330 cubic feet of sand. If the sandbox is 3 feet tall, and 10 feet wide, what is the length of the sand box?
Answer:
We are given that the total volume of the sandbox is 330 cubic feet.
We are given the side measurements of 3 feet tall and 10 feet wide.
3 x 10 = 30 sq2
V(volume)= 330 ft3
330 ft3 divided by 30 sq2 = 11ft
In conclusion, the length of the box would be:
= 11 ft
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Is (3, -5) a solution to this system of equations?
y = -1/3x - 4
y = -2x + 1
Yes or No
Answer: Yes
Step-by-step explanation:
Solve the system of equations by setting the two substituting the first y equation in for the second and getting: -1/3x - 4 = -2x + 1.
Now, add 2x to the left side to cancel it from the right and add 4 to the right side to cancel if from the left to get: (5/3)x = 5
Solve for x to get 3.
Plug x into the second equation (could be either equation though) and get: y = -2(3) = 1 = -5.
Thus, (3,-5) is a solution :)
jimmy has 27 apples and there are 9 houses. he feeds the same number of apples to each horses. how many apples dose jimmy feed to each horse?
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Answer:
The answer is, Jimmy, fed the horses 3 apples each.
27 apples divided into the 9 horses
27 ÷ 9 = 3
If you had 27 seven apples and you individually gave one apple to each of the 9 horses each horse would end up having 3.
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Gobe weighs 53.6 kg. he wears shoes which weigh 450 gm and carries a school bag weighing 4.5 kg. if he stands on the scales in his shoes and carrying the school bag. what weight will be recorded?
Answer:
58.55Kg
Step-by-step explanation:
450 in Kg is 0.45.
0.45 + 4.5 = 4.95. 4.95 + 53.6 = 58.55.
The line through the points (6, 3) and (4, –5) is perpendicular to the line through which of the following points?
Answer:
Step-by-step explanation:
( 6 , 3 )
( 4 , - 5 )
m = [tex]\frac{-5-3}{4-6}[/tex] = 4
The slope of the perpendicular line is opposite reciprocal or [tex]-\frac{1}{4}[/tex] , so, the answer is (a).
n the past you paid $800 per month to rent your apartment. You now pay $900 per month for your rent. What is the percent increase in your rent?
Answer:
12.5%
Step-by-step explanation:
900 - 800 = 100
Gotta pay $100 more
100 / 800 = 0.125
I need help, I will give brainliest
what is the value of x, round to the nearest 10th.
use sin, cos, and tan
What is the value of y?
у
60°
80°
Answer: 40
Step-by-step explanation:
The angles form a straight angle, so y = 180 - 80 - 60 = 40.
Mia had 5000 In the bank. She keeps the money in the bank for 4 years at 5% interest. How much interest did she earn?