At a large high school, 20% of the students prefer to have a salad for lunch. What is the probability that you must ask four people before you find someone who would prefer a salad for lunch? (The fifth person says yes)

The dot plot where each dot represents a friend is given below

We are given that;

Number of siblings= 4,1,0,3,2, 2

Now,

To create a dot plot using this data, we need to follow these steps:

Draw a horizontal number line with the values from 0 to 4, which are the possible numbers of siblings that Sarah’s friends have. Label the number line as “Number of siblings”.

For each value in the data set, place a dot above the corresponding number on the number line. If there are more than one friend with the same number of siblings, stack the dots vertically.

Give the dot plot a title, such as “Number of Siblings of Sarah’s Friends”.

The dot plot should look something like this:

Therefore, by the dot plot is shown above.

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The equation of the hyperbola with center (-10, 5), a focus at (-10, 15),

and a co-vertex at (-18,5) is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

From the question, we are to determine the equation of the hyperbola with the given center, focus and co-vertex.

The equation of a hyperbola with center (h, k), a focus at (h, k + c), and a co-vertex at (h + b, k) is given by

[(y - k)² / a²] - [(x - h)² / b²] = 1

Where a² = c² - b²

From the given information,

The center of the hyperbola is (-10, 5)

Thus,

h = -10, k = 5

The focus is at (-10, 15)

By comparison with (h, k + c)

k + c = 15

5 + c = 15

c = 15 - 5

c = 10

The co-vertex is at (-18, 5)

By comparing with (h + b, k)

h + b = -18

-10 + b = -18

b = -18 + 10

b = -8

From the formula a² = c² - b²

Then,

a² = c² - b²

a² = 10² - 8²

a² = 100 - 64

a² = 36

Now,

We can write the equation of the hyperbola

[(y - k)² / a²] - [(x - h)² / b²] = 1

Substitute the values

[(y - (5))² / (36)] - [(x - (-10))² / (-8)²] = 1

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

Hence,

The equation of the hyperbola is:

[(y - 5)² / 36] - [(x + 10)² / 64] = 1

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Answer:

3 1/2 is located between 3 and 4 on the number line.

Answer:

x + (x+2) = 124

Step-by-step explanation:

Let x be the first odd number, then the next consecutive odd number would be x+2.

According to the problem, the sum of these two numbers is 124.

So, we can set up the following equation:

x + (x+2) = 124

Simplifying this equation:

2x + 2 = 124

Subtracting 2 from both sides:

2x = 122

Dividing both sides by 2:

x = 61

Therefore, the first odd number is 61, and the next consecutive odd number is 63.

To check, we can add them together:

61 + 63 = 124

So the solution is x = 61.

Answer:

x + x + 2 = 124

(and then you could solve that x=61 and the two numbers are 61 and 63)

Step-by-step explanation:

"sum" means adding. "consecutive" means the two numbers are in a row, or one right after the other. Like 3 and 4 are consecutive numbers and 3 and 5 are consecutive odd numbers. 3 and 11 are not consecutive.

So let one number be x.

Then next odd number after that is +2...so the 2nd number is x+2.

And they add up to 124. Write the equation like this:

 x + x + 2 = 124

If you want or need to solve then:

combine like terms.

2x +2 = 124

subtract 2.

2x = 122

divide by 2.

x = 61

then x+2 is 63.

Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

Compound interest is the term for interest that is earned on interest.

This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.

At the end of the second year, you will have $110.25.

So, we know that:
Principal amount = $25000

Interest rate = 4.7%

Time = 2 years

Compounded annually

Then, using the compounding calculator:

(Refer to the graph attached below)

The amount after 2 years will be $27,405.23.

Interest in this is:
$27,405.23 - $25,000

$2,405.23

Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

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Correct question:

Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.

Answer:

A. 500 cm3

Step-by-step explanation:

The general inverse variation equation is

y = k/x, where y varies inverse as x and k is the constant of proportionality.

Thus, if we substitute V for y and P for x in the equation, we have

V = k / x

To find k, we can plug in 80 for V and 2000 for P and solve for k:

80 = k / 2000

160000 = k

Finally, to find V when P = 320 millimeters, we can plug in 160000 for k and 320 for P and solve for V:

V = 160000 / 320

V = 500 cm3

The function f(x) = a(b^x) is an exponential function, where "a" is the initial value or y-intercept of the function, and "b" is the base of the exponent, which determines the rate of growth or decay.

When x = 0, we have:

f(0) = a(b^0)

Since any number raised to the power of 0 is 1, we can simplify the expression to:

f(0) = a(1) = a

Therefore, when x is equal to 0, the value of the function is just the initial value "a". This is true for any exponential function of the form f(x) = a(b^x).

In other words, the initial value of an exponential function is the value of the function when x = 0, and in this case, that value is just "a".

Answer: B: [tex]f(x) = x^2 - 4x-5[/tex]

Step-by-step explanation:

Lets write this first in vertex form:

We know the vertex of this function is at (2, -9)

this gives us h,k values. Since there is no stretch or compression, and no negative coefficient we can simply plug in:

f(x) = [tex](x-2)^2 - 9[/tex]

Expanding this, we get answer B.

This tetrahedron is known as a triangular pyramid and it has four triangular faces, four vertices, and six edges.

We can name the faces of the triangular prism as:

The edges would be:

The faces would be:

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Answer:

40°

Step-by-step explanation:

360-240=120

120÷3=40°

Answer

40°

Add of all angles would be 360° .

so equation would be

360° - 240° = 3x

360 - 240 is 120

so

120 = 3x

Dive the both sides of equation by 3 (*just to make it simple and clear. you cam just move 3 to other side of equation . since its multiplied in its side, it would change to division*)

120/3 = 3x/3

40° = x

all the X angle would be 40°

240 + 40 + 40 + 40 = 360°

The two lengths of the chords of circle are solved and x = 5 units

Given data ,

Let the length of the two chords be represented as AB and CD

Now , AB = 21 and CD = 3x

where E is the extended point of the two chords which intersect at point E

Now , from the intersection of chords outside the circle ,

BE ( AE ) = DE ( CE )

On simplifying , we get

4 ( 25 ) = x ( 4x )

100 = 4x²

Divide by 4 on both sides , we get

x² = 25

Taking square roots on both sides , we get

x = 5 units

Hence , the chords are solved and x = 5 units

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Answer:

3 and 4

Step-by-step explanation:

- 2 < x < 5

has solutions x = - 1, 0, 1, 2, 3, 4

x > 2

has solutions

x = 3, 4, 5, 6, ...........

the integer values that satisfy both are x = 3, 4

Answer:

- The centers of the distributions should be similar

Step-by-step explanation: - The centers of the distributions should be similar

Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

[tex]a=\pi r^{2}[/tex]

[tex]a=\pi (19)^{2} =361\pi[/tex]

[tex]a=1134.11cm^{2}[/tex]

Hope this helps

The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².

It follows from the task content that the total area of the roof as given in the task content is to be determined.

On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.

Therefore;

Area = (71 × 39) - (15 × 8)

= 2649 ft².

Ultimately, the total area measure of the roof in square feet is; 2649 square feet.

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The solution to the equation 57 = 2070(0.93)^x - 11 to the nearest tenth is x ≈ 86.5.

A mathematical assertion that two expressions are equal is known as an equation.

A typical equation contains one or more variables, which are elements with several possible values.

Finding the values of the variables that make an equation true is the aim of equation solving.

A linear equation, which has the form:, is the most widespread sort of equation.

ax + b = 0

where the objective is to find the value of the variable x and a and b are constants.

A variable in mathematics is a symbol or letter that designates a value that is subject to variation or change. In algebraic expressions and equations, variables are used to denote unknown or fluctuating quantities, such as a building's height or the number of apples in a basket.

Typically, letters from the alphabet, such as x, y, and z, are used to represent variables. Mathematical expressions can be created using variables, constants (numbers), and operators (+, -, x, /, etc.) in an algebraic expression. As an illustration, the phrase 2x + 3y - 5z combines the three variables x, y, and z in a linear fashion.

According to the question ,

By adding 11 to both sides, we may isolate the exponential term first:

57 + 11 = 2070(0.93)^x

Streamlining the left side: 68 = 2070(0.93)^x

By 2070, divide both sides: 0.03285024 = (0.93)^x

Using both sides' natural logarithms: ln(0.03285024) = ln[(0.93)^x]

By applying the logarithm property, which states that ln(ab) = b ln(a):

ln(0.03285024) = x ln(0.93)

By dividing both sides by ln(0.93), one can find x:

x = ln(0.03285024) / ln(0.93)

When we evaluate this expression with a calculator, we obtain:

x ≈ 86.5

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Answer:

$25.10

Step-by-step explanation:

We can find the total amount Andrew spent at the hockey game by finding the sum of each individual cost, including the costs for admission, the program, the popcorn, and the large drink

Total amount spent = 13.50 + 4.75 + 3.50 + 3.35

Total amount spend = $25.10

Answer: >$15

Step-by-step explanation: She needs at least $15, so, we use the greater then symbol, because she’ll be fine if she has more than $15(>15) but she won’t be able to buy the ticket if she has under $15(<15)

Answer: D (t−3)(t−5)(t+4)

Step-by-step explanation:

Hope this helps! :)

the discount on the dog food is $0.27, and the discounted price is $1.08.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:

Discount = 20% of $1.35

Discount = 0.20 x $1.35

Discount = $0.27

Therefore, the discounted price of the dog food would be:

Discounted price = Original price - Discount

Discounted price = $1.35 - $0.27

Discounted price = $1.08

So the discount on the dog food is $0.27, and the discounted price is $1.08.

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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The solution for the inequality -2(8x - 4) < 2x + 5 is x > 1/6.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let's simplify the inequality -

-2(8x - 4) < 2x + 5

Distribute the -2 -

-16x + 8 < 2x + 5

Subtract 2x from both sides -

-18x + 8 < 5

Subtract 8 from both sides -

-18x < -3

Divide both sides by -18, remembering to reverse the inequality because we're dividing by a negative number -

x > 3/18

Simplifying, we get -

x > 1/6

Therefore, the solution to the inequality is -

x > 1/6

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Answer:

XY = 7.5 cm

Area = 105 cm²

Step-by-step explanation:

First, let us use the sin Θ to find the value of XY.

Sin Θ = Opposite ÷ Hypotenuse

Sin 43 = XY ÷ 11

0.6819 = XY ÷ 11

0.6819 × 11 = XY

7.5 cm = XY

The formula to find the area of the triangle is:

[tex]\sf Area=\frac{1}{2}*base*height\\\\\sf Area=\frac{1}{2}*28\:cm\:*7.5\\\\Area=105\:cm^2[/tex]

Answer:

140° + 90° + 90° + k = 360°

320° + k = 360°

k = 40°

Therefore , the solution of the given problem of angles comes out to be k has a value of 40 degrees.

The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.

Here,

According to the information provided, it seems that there is a 140° angle followed by an angle designated as "k". These two angles appear to be adjacent, and since the sum of all angles on a straight line is 180 degrees, we may construct the following equation:

=> 140° + k = 180°

We can now calculate the value of k as follows:

=> k = 180° - 140°

=> k = 40°

So, "k" has a value of 40 degrees.

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Therefore, the balance in Larry's savings account at the end of 8 years is $1,699.84.

Algebra. A financial management expert is often required to solve for variables in banking and investing financial models. Even if most of the work is now done for us by programmes like Excel, having a solid grasp of the fundamentals of algebra is still commonly seen as being very beneficial.

After eight years, the balance in Larry's savings account can be determined using the straightforward interest formula:

A = P(1 + rt)

where A represents the final balance, P the initial principal, r the yearly interest rate expressed as a decimal, and t the period of time in years.

In this case, we have P = $1,287, r = 0.04, and t = 8.

A = $1,287(1 + 0.04*8)

= $1,287(1.32)

= $1,699.84

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The critical value is Z = 2.331. The rejection region is Z > 2.33

What is meant by critical value?

A critical value is a value used in hypothesis testing to determine whether to reject or fail to reject the null hypothesis.

What is meant by rejection region?

The rejection region is the set of values that lead to the rejection of the null hypothesis in favor of the alternative hypothesis.

According to the given information

To find the critical value(s) and rejection region(s) for a right-tailed z-test with level of significance x = 0.01, we can use the following formula1:

Critical value: Z = Zα where α = x and Zα is the Z-score that corresponds to an area of α in the standard normal distribution table

Rejection region: Z > Zα

For a right-tailed test with α = 0.01, we can find the critical value using a standard normal distribution table1. The critical value is Z = 2.331. The rejection region is Z > 2.33

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Answer:

The given line has a slope of 1/4. The slope of any line perpendicular to this line will have a slope equal to the negative reciprocal of 1/4, which is -4.

We are also given that the line passes through the point (0, 2). Using point-slope form, we can write the equation of the line as:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (0, 2). Substituting the values, we get:

y - 2 = -4(x - 0)

Simplifying, we get:

y - 2 = -4x

Adding 2 to both sides, we get the final equation of the line:

y = -4x + 2

Therefore, the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5 is y = -4x + 2.

Answer:

6-x-2x^2 - (-2x^2 +3x+2)=6-x-3x-2=-4x+4