Answer:
16, 26, 36Step-by-step explanation:
[tex]a_1=-24\\a_2=-24+10=-14\\a_3=-14+10=-4\\a_4=-4+10=6\\\\\text{Add the common difference d = 10 to the previous term.}\\\\a_5=a_4+10\to a_5=6+10=16\\a_6=a_5+10\to a_6=16+10=26\\a_7=a_6+10\to a_7=26+10=36\\\vdots[/tex]
How to rename 8 2/3 = 7 ?/3
let's firstly convert the mixed fractions to improper fractions and proceed from there.
[tex]\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}~\hfill \stackrel{mixed}{7\frac{x}{3}}\implies \cfrac{7\cdot 3+x}{3}\implies \stackrel{improper}{\cfrac{21+x}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{26}{3}=\cfrac{21+x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{26}{3} \right)=3\left( \cfrac{21+x}{3} \right)}\implies 26=21+x\implies \boxed{5=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\frac{2}{3}=7\frac{5}{3}~\hfill[/tex]
7 5/3 if that’s what your asking
8 2/3 is equal to 7 5/3
a bottle holds z ounces of water. a second bottle holds 16 ounces, which is 8/5 times as much water. how much does the first bottle hold?
Answer:
10 ounces of water
Step-by-step explanation:
16=8/5
z=1
16*1=16
8/5*z=8/5z
16=8/5z
16/1.6z=10
z = 10
Answer:
10 ounces of water
Step-by-step explanation:
Write an equation to describe the variation. Use k for the constant of proportionality.
y varies directly as u and inversely as p^4
[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{y} varies directly as \underline{u} and inversely as }p^4}{y=\cfrac{ku}{p^4}}[/tex]
Carter wants to know if warming up will help runners sprint faster. Thirty track and field athletes volunteered to participate in his study. He randomly assigns 15 athletes to warm-up for 10 minutes. All 30 participants sprint the same distance. He calculates the mean for each group and determines that the mean for the warm-up group was 10.7 seconds, and the mean for the other group was 13.2 seconds. To test the difference of means he re-randomized the data 54 times, and the differences are plotted in the dot plot below. What can Carter conclude from his study?
The graph shows: (3) -2.5, (6) -2.0, (9) -1.5, (12) -1.0, (6) -0.5, (4) 0.0, (3) 0.5, (7) 1.0, (3) 1.5, and (1) 2.0. The parenthesis is how many dots there is at each point.
The difference in the means is significant because a difference of 2.5 is very likely.
The difference in the means is not significant because a difference of 2.5 is very likely.
The difference in the means is significant because a difference of 2.5 is not very likely.
The difference in the means is not significant because a difference of 2.5 is not very likely.
Answer:
The answer is actually C. here's proof:
It also makes sense since 2.5 is very unlikely, so the change is significant.
Kamal solved an equation as shown below. 3(x-8)=x+2x+7 3x-24=3x+7 -24=7 What is the solution to Kamal’s equation?
There is no solution to Kamal's equation because -24 ≠ 7
How to solve the problem
The equations are given as
i. 3(x-8)=x+2x+7
ii. 3x-24=3x+7
iii. -24=7
We have to expand the first equation
3(x-8)=x+2x+7
this would produce the second equation
3 * x - 3 * 8 = 3x + 7
we have
ii. 3x-24=3x+7
from here we have to take like terms on put them on same side
3x - 3x = 7 + 24
0 = 31
or from 3x-24=3x+7
the 3x is eliminated
-24 = 7
But we know that -24 ≠ 7. Hence no solution.
Which expression shows how to convert 60 hours to days?
Answer:
2.5 Days
Step-by-step explanation:
Answer:
2.5 days
Step-by-step explanation:
A spinner is divided into 5 sections.You spin the spinner once. there are 2 parts in the white section and 3 parts in the dark.
* Find the probability that the spinner lands on a white section.
*Find the probability that the spinner lands on a dark section
Answer:
White: 2/5
Dark: 3/5
Step-by-step explanation:
There are 5 sections and there are 2 white spots and 3 dark spots.
So, 2 out of the 5 sections are white which is 2/5 and 3 out of the 5 sections is dark which is 3/5.
Answer:
The probability that the spinner lands on a white section is [tex]\frac{2}{5}[/tex] .The probability that the spinner lands on a dark section is [tex]\frac{3}{5}[/tex] .Step-by-step explanation:
Given : The total number of sections = 5
The number of white sections = 2
The number of dark sections =3
Now, the probability that the spinner lands on a white section is given by :-
[tex]\text{P(white)}=\dfrac{\text{Number of white sections}}{\text{total sections}}\\\\=\dfrac{2}{5}[/tex]
Now, the probability that the spinner lands on a dark section is given by :-
[tex]\text{P(dark)}=\dfrac{\text{Number of dark sections}}{\text{total sections}}\\\\=\dfrac{3}{5}[/tex]
Please help me it’s urgent
Answer:
the answer would be y=2x+4
Step-by-step explanation:
A circle has its center at (6,-3) and a radius of 5 units. What is the equation of
the circle?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{5}{ r}\\[2em] [x-6]^2+[y-(-3)]^2=5^2\implies (x-6)^2+(y+3)^2=25[/tex]
Answer:
Step-by-step explanation:
The x value for the center is part of the x^2 part of the equation.
The y value for the center is part of the y^2 part of the equation.
The radius is squared.
(x - 6)^2 + (y + 3)^2 = 5^2
Notice the sign change for the center. When you move horizontally the sign of the center changes sign in the circle's equation.
The graph is included to show you that.
Evaluate the following expression (-5+7x1)-9x5
Final answer:
To evaluate the expression (-5+7x1)-9x5, follow the order of operations: calculate inside the parentheses, multiply, and then subtract, resulting in a final answer of 47.
Explanation:
To evaluate the expression (-5+7×1)-9×5, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break down the expression step by step:
Inside the parentheses: -5 + (7 × 1) = -5 + 7 = 2.
Multiply: -9 × 5 = -45.
Subtract the value obtained from step 2 from the result of step 1: 2 - (-45).
Change the subtraction of a negative value to addition: 2 + 45 = 47.
Thus, the expression (-5+7×1)-9×5 evaluates to 47.
Mese questions are based on a 52
a ck without Jokers.
1) Find the probability of drawing cards 2 through
2) Find the probability of drawing a face card that is a Diamond.
3) Find the probability of drawing a 7 of Clubs.
4) Find the probability of drawing a face card.
5) Find the probability of drawing a face card that is red.
6) Find the probability of drawing a red card.
7) Find the probability of drawing a 5.
8) Find the probability of drawing a Diamond 6 through 9.
9) Find the probability of drawing a Diamond.
10 ) Find the probability of drawing black cards 2 through 8.
someone tell me the answers asap.it will help me hell.
Answer:1.) 6/52
Step-by-step explanation:
The answer provides step-by-step solutions to a set of 10 different probability questions based on a standard deck of 52 playing cards. Each solution follows the same basic principle of dividing the number of ways the desired outcome can occur by the number of total possible outcomes.
Explanation:The probability calculations, based on a 52-card deck, are as follows:
The probability of drawing cards 2 through 10 is 9 cards/suit * 4 suits/52 cards = 36/52 or 9/13.The probability of drawing a face card that is a Diamond is 3 face cards in the Diamond suit/52 cards = 3/52 or 1/17.The probability of drawing a 7 of Clubs is 1 card/52 cards = 1/52.The probability of drawing a face card (Jack, Queen, or King) is 3 face cards/suit * 4 suits/52 cards = 12/52 or 3/13.The probability of drawing a red face card is 6 red face cards/52 cards = 6/52 or 3/26.The probability of drawing a red card is 26 red cards/52 cards = 26/52 or 1/2.The probability of drawing a 5 is 4 cards (one from each suit) /52 cards = 4/52 or 1/13.The probability of drawing a Diamond 6 through 9 is 4 cards in the Diamond suit/52 cards = 4/52 or 1/13.The probability of drawing a Diamond is 13 cards in Diamond suit/52 cards = 13/52 or 1/4.The probability of drawing black cards 2 through 8 is 14 black cards (7 in each black suit)/52 cards = 14/52 or 7/26.Remember that probabilities are calculated as the desired outcome divided by the total possible outcomes.
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if Mark wants to see how the price of gas has increased over the last five years, which type of graph would best illustrate this data line graph circle graph bar graph pictograph
Line graph because it shows differences
Problem Page A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 1.5 cm. If silver is priced at $6.00 per cm3 , how much will the silver cost to make one solid sphere? Use 3.14 for pi, and do not round your answer.
Answer:
84.78
Step-by-step explanation:
Final answer:
To determine the cost of silver needed for a solid sphere with a radius of 1.5 cm, the volume is calculated first, and then multiplied by the cost per cubic centimeter of silver, resulting in a total cost of $84.78.
Explanation:
The problem requires calculating the cost of the silver needed to manufacture a solid sphere. To find the cost, we first need to calculate the volume of the sphere using the formula V = (4/3)πr³, where V is the volume and r is the radius. Then, we multiply the volume by the cost per cubic centimeter of silver to get the total cost.
Given the radius r = 1.5 cm and the cost of silver = $6.00/cm³, we can plug these values into the formula:
Calculate the volume of the sphere: V = (4/3)π(1.5 cm)³Compute the volume: V = (4/3)π(3.375 cm³) = (4/3)π×3.375 cm³ = 4π×1.125 cm³ = 14.13 cm³ (using 3.14 for π)Calculate the cost: Cost = 14.13 cm³ × $6.00/cm³ = $84.78Therefore, the silver required to make one solid sphere would cost $84.78.
What is the series using summation notation?
36+69+102+...+267
first term =36
second term=69
So common difference=69-36=33
checking. 69+33=102
36=3+33
so the series in AP Becomes as...
(3+33) ,(36+33) ,(36+2(33)) ... (36+7(33))
So The Answer is...
(refer above attachment.)
Hope it helps...
Regards,
Leukonov/Olegion.
I need help please
Answer:
b
Step-by-step explanation:
it makes sense because they all are going down by 1 side each time
B) the triangle because each figure is loosing one side
Round 96 cent. Amount. To the nearest dollar
Answer:
About 1 dollar.
Step-by-step explanation:
First we must establish the possible values that 96 cents can be rounded to.
We know that 96 cents is more than nothing, or 0. We also know that a dollar is 100 cents. This means 96 cents is in between 0 and 1 dollar. We just have to determine whether 96 is closer to 100 cents or 0 cents.
To do this find the difference between 96 and each value.
100-96 = 4
96-0 =96
The difference between 96 and 100 is smaller, so the values are closer and 96 should be rounded to a dollar.
Write the expression in terms of cosine. Please help.
Answer:
sin(81)
Step-by-step explanation:
Since the sine of something is the ratio of the opposite side to the hypotenuse, to get the same ratio in cosine, you take the complement of the angle. So the answer is sin(90 - 9) or sin(81).
The expression in terms of cosine cos 81°. The expression is obtained by the trigonometric rules.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The given expression is;
sin9°
The expression in terms of cosine.
sin 9°= sin(90-81°)
sin 9°= cos 81°
Hence,the expression in terms of cosine cos 81°.
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Maria want to make a footstool in the shape of a cylinder, as show below. She wants to fill the footstool with foam and cover it with fabric. r=12in by h=18in
Answer:
She'll need 8143 cubic inches of foam and 1,809.6 square inches of fabric.
Step-by-step explanation:
Assuming you want to know how much foam and fabric she will need...
First the foam... so we need to determine the volume of that footstool. The Volume of a cylinder is given by:
V = π * r² * h
So, we plug in the numbers:
V = π * 12² * 18 = π * 144 * 18
V = 2,592 π = 8143 cubic inches.
Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.
The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool. The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.
So the lateral surface of the cylinder is:
LS = 18 * 75.14 = 1,357.2 sq inches.
Then we need to calculate the area of the top... which is easy:
A = π * r² = π * 12² = 144 π = 452.4 sq inches
So, to cover the lateral side of the footstool and its top, she needs to use:
TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.
Answer:
The fabric needed = 2260.8 square inches
Step-by-step explanation:
Points to remember
Surface area of cylinder = 2πr(r + h)
It is given that,
Maria want to make a footstool in the shape of a cylinder.
radius of cylinder = 12 in and height = 18 in
To find the surface area
Here r = 12 in and h = 18 in
Surface area = 2πr( r + h)
= 2 * 3.14 * 12 (12 + 18)
= 2260.8 square inches
What is the approximate value of f(5) for the function f(x)=6.87(2.5)(x – 1)?
Answer:
68.7
Step-by-step explanation:
We need only estimate (approximate) the value of f(x) at x = 5:
f(x)=6.87(2.5)(x – 1) → f(5)=6.87(2.5)(5 – 1).
Note that 2.5(4) = 10, so now we have (exactly) f(5)=6.87(10), which, in turn, is
equal to 68.7.
There 1,195 souvenir paperweights that need to be packed in boxes. Each box will hold 13 paperweights. How many boxes will be needed
Answer:
92
Step-by-step explanation:
You need to divide the total number of souvenir paperweights divded by how much the box holds.
You will get 91.923 however you cant have only part of a box so you have to round up to 92.
Which trigonometric function is being used if we get the fraction 6/10 as our answer? Question 3 options: sin(A) cos(A) tan(A) tan(gerine)
Answer:
cos(A)Step-by-step explanation:
For angle A we have
opposite = 8
adjacent = 6
hypotenuse = 10
sin A = opposite/hypotenuse
cos A = adjacent/hypotenuse
tan A = opposite/adjacent
cot A = adjacent/opposite
6/10 = adjacent/hypotenuse = cos A
The trigonometric function of the triangle is given by cos A = 6/10
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
where the measure of ∠ABC = 90°
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
So , on simplifying , we get
The measure of BC = 6 units
The measure of AB = 8 units
The measure of AC = 10 units
cos A = 6 / 10
Hence , the measure of cos A of triangle is cos A = 6 / 10
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What is the area, in square inches, of the figure shown here?
25 POINTS PLEASE HELP A parallelogram with a height of 2 inches is shown. The height of the parallelogram is used to divide the side of the parallelogram into 5 inches, which is the length (or side) of the rectangle, and into 2 inches, which is the base of the triangle formed by the division.
10 in2
14 in2
16 in2
20 in2
Answer:
B.[tex]14in^{2}[/tex]
Step-by-step explanation:
Solve this by using one of two methods.
Split up into different shapes:
This method uses the sum of the areas of a rectangle and two triangles to find the area of the parallelogram:
[tex]A=(b*h)_{rectangle} +2*(0.5*b*h)_{triangle} \\A=(5*2)+2(0.5*2*2)\\A=10+4\\A=14in^{2}[/tex]
Use Parallelogram formula:
This formula is the same as the formula for a rectangle where you multiply the base by the height.
[tex]A=b*h\\A=(5+2)*2\\A=14in^{2}[/tex]
Answer: The answer is 14 in2
Triangle ABC is dilated so that the side lengths of the image are three times the lengths of their corresponding sides. Which of the following statements are true? Select all that apply.
AB ≅ A'B'
CB ~ C'B'
∠A ≅ ∠A'
CA ≅ C'A'
∠B ~ ∠B'
Answer:
∠A ≅ ∠A' and CB ~ C'B'
Step-by-step explanation:
In a dilation, you get a SIMILAR figure. It will have the same shape, but a different size.
Similar figures have the same angle measures but the side lengths will change.
Any of the answers with congruent (≅) angles are correct:
∠A ≅ ∠A'
Any of the answers with SIMILAR (~) side lengths are correct:
CB ~ C'B'
Answer:
∠A ≅ ∠A' and CB ~ C'B'
Step-by-step explanation:
Glowmart marked down it's stock 32%. What will be the sale price of a $60 jacket
Answer: $40.80
Explanation: 60*.68=40.8
Answer:
Sale price = $40.80
Step-by-step explanation:
The original price = $60
After mark down of 32% is applied,
The selling price becomes 100% - 32% = 68%
The selling price = 68% of $60 = [tex]\frac{68}{100}[/tex] × $60 = $40.80
What is the value of 8P4? A. 32 B. 70 C. 1680 D. 4096
P means permutation, so using the permutation formula:
8P4 = 8! / (8-4)!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)
= 8 x 7 x 6 x 5
= 1680
The answer is C.
Answer:
C
Step-by-step explanation:
Its C
Find the value of x. Please help
18/25= 21/x
18x=525
525/18 = 29.16
29.4
I don't know how to graph y=6/5x+1
can someone help me?
So this equation is in slope intercept form:
y = mx + b
m is slope
b is y-intercept
This means that for this equation the slope is 6/5 and the y-intercept is (0 , 1)
Look at image below for the graph
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE ANSWER THIS AND EXPLAIN HOW YOU GOT THE ANSWER.
9 - 3 ÷ 1/3 + 1 =
Answer:
Step-by-step explanation:
If you use pemdas, you would do 3÷1/3 which equals 9. Then do 9-9, which equals 0. Then, do 0+1, which equals 1. Hope this helps! <3
[tex]9 - 3 \div \frac{1}{3} + 1 = [/tex]
Divisions go first, to do it we have to reverse the fraction and turn ÷ into ×
[tex] = 9 - 3 \times 3 + 1 = [/tex]
Now the multiplication
[tex] = 9 - 9 + 1 = [/tex]
[tex] = 1[/tex]
anyone can solve this question?
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
2x + y = 4 → (2)
Rearrange (2) expressing y in terms of x by subtracting 2x from both sides
y = 4 - 2x → (3)
Substitute y = 4 - 2x in (1)
x² + (4 - 2x)² = 5 ← expand factor on left side
x² + 16 - 16x + 4x² = 5
5x² - 16x + 16 = 5 ( subtract 5 from both sides )
5x² - 16x + 11 = 0 ← in standard form
(5x - 11)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)
x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]
Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )
Two stores have movies to rent
The first store charges a $12.50-per-month membership fee plus
$1.50 per movie rented
The second store has no membership fee but charges $3.50 per movie
rented.
What is the minimum number of movies a person would need to rent in a month
for the first store to be a better deal?
Answer:7
Step-by-step explanation:
In the first store, you pay 12.5+1.5x per x movies
In the second store, you pay 3.5x per x movies
The first store offers a better deal when:
12.5 + 1.5x > 3.5x
12.5 > 2x
6.25 > x
Which means if you rent minimum 7 movies in month, you should go to the first store
Answer:
7Step-by-step explanation:
We know that the first store charges $12.50 per month, which is a initial condition, and charges additionally $1.50 per movie, which is variable, this represents the ratio of change, so this can be expressed as
[tex]\$12.50 + \$1.50x[/tex]
Where [tex]x[/tex] represents movies.
Now, the second store doesn't charge and membership fee, just it charges a cost per movie which is $3.50.
Then, to solve the minimum number of movies needed to Plan A be the best choice, we just have to solve the following inequality
[tex]\$12.50 + \$1.50x> \$3.50[/tex]
Which expresses the case where Plan A is a better choice, solving for [tex]x[/tex], we have
[tex]\$12.50 + \$1.50x> \$3.50x\\\$1.50x - \$3.50x >-\$12.50\\(-1)(-2x)>(-12.50)(-1)\\2x<12.50\\x<\frac{12.50}{2}\\ x<6.25[/tex]
Which means that the minimum number of movies is 7, which is the next whole number after 6.