7. What is an expression equivalent to 5(3x+2) using the distributive property?

hurry i need help pleas

Step-by-step explanation:

9868866858566586575765578

Answer:

32

Step-by-step explanation:

The area of a parallelogram is bh where b = base, h = height

This is one of the questions where plotting the points and seeing the parallelogram is vital

See the attached figure

height h = |difference between x-coordinates of A and C| =

= |6 - 2| = 4.

This will be the same as |difference between x-coordinates of B and D

base b = |difference between y-coordinates of A and B| =  |1-(-7)| = 8.

This will be same as |difference between y-coordinates of C and D|

Area = bh = 8 x 4 = 32

(a) P( Type -I error) = P (rejecting \(H_0\) |  when  \(H_0\) is true )

(b)  P( Type -II error)= P(not rejecting  \(H_0\) |  when  \(H_0\) is false )

Given,

In the question:

We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin.

To find the:

a) the value of α

b) the value of β if p = .7

Now, According to the question:

Hypothesis Testing:

The hypothesis testing evaluates two mutually exclusive statements about the population parameters to determine which statement is correct among them. There are two types of error :

1. Type -I

2. Type -II

The data is given as:

X ~ Bin(36, p)

\(H_0:p = 0.5\\\\H_1:p \neq 0.5\)

(a) P( Type -I error) = P (rejecting \(H_0\) |  when  \(H_0\) is true )

                               = P(|X- 18| \(\geq\) 4 ; p = 0.5)

                               = 1 - {P(14 < X < 22)}

                               = 1 - {P(X < 22) - P(X < 14)}

                                = 1 -  {P(X ≤ 21) - P(X ≤ 13)}

                                = 1 - {0.87851 - 0.066249}

                                = 0.18774

(b)  P( Type -II error)= P(not rejecting  \(H_0\) |  when  \(H_0\) is false )

                                  = P(|X- 18| \(>\) 4 ; p = 0.7)

                                  = P(14< X < 22)

                                  =  P(X < 22) - P(X < 14)

                                  =  P(X ≤ 21) - P(X ≤ 13)

                                  = 0.091662 - 0.018322

                                  = 0.07334

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Answer:

$12 per hour

Step-by-step explanation:

\(6\frac{1}{4}\) hours =6.25 hours

per hour payment=paid/hours=75/6.25=12

The set of vectors that form an

orthonormal basis

for R² is B. {[1,0]ᵀ,[0,1]ᵀ}.

To determine which of the sets of vectors form an orthonormal basis for R², we need to check if the vectors are orthogonal and have a length of 1. For set A, we can calculate the dot product of the two vectors and see that it is not equal to zero, so they are not orthogonal. For set C, the dot product of the two vectors is also not equal to zero, so they are not orthogonal. For set D, we can calculate the length of the vectors and see that they are not equal to 1, so they do not have a length of 1. Therefore, the only set of vectors that form an orthonormal basis for R² is set B, which consists of the standard basis

vectors

{[1,0]ᵀ,[0,1]ᵀ}.

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Answer: x = -3

Step-by-step explanation: Isolate the variable by dividing each side by factors that do not contain a variable.

I hope this helps you out. :)

Answer:

x=−3

Step-by-step explanation:

8x+11−3x=2x+2

Step 1: Simplify both sides of the equation.

8x+11−3x=2x+2

8x+11+−3x=2x+2

(8x+−3x)+(11)=2x+2(Combine Like Terms)

5x+11=2x+2

5x+11=2x+2

Step 2: Subtract 2x from both sides.

5x+11−2x=2x+2−2x

3x+11=2

Step 3: Subtract 11 from both sides.

3x+11−11=2−11

3x=−9

Step 4: Divide both sides by 3.

3x

3

=

−9

3

x=−3

The number of ways to order the first, second and third place finishers is simply the number of permutations of 8 runners taken 3 at a time. This can be calculated using the formula for permutations

The formula for permutations, P(n,r), gives the number of ways to choose r items from a set of n items, where order matters. This formula is calculated as:

P(n,r) = n! / (n-r)!

where n! represents the factorial of n (i.e. n multiplied by n-1 multiplied by n-2, etc. down to 1).

In this problem, n = 8 and r = 3, so the number of permutations is:

P(8,3) = 8! / (8-3)! = 8! / 5! = 40320 / 120 = 336

So there are 336 different arrangements of first, second, and third place finishers in the 100-meter sprint.

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No. The given values: 4¢ per 21 units and 11¢ per 43 units is found to be not a ratios equivalent.

"Two maybe more ratios that reflect the same correlation or compare of numbers are recognized as equivalent ratios," according to the definition of equivalent ratio. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios. Even if the values of the antecedent and the consequent are different, if we simplify them, we will still arrive at the same value.

Given data:

4¢ per 21 units = 4:21

11¢ per 43 units = 11:43

Determine whether the ratios of 4:21 and 11: 43 are comparable.

Thus, the given values: 4¢ per 21 units and 11¢ per 43 units is found to be not a ratios equivalent.

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

a.2x

b.2x+4

c.3x

Step-by-step explanation:

We know that x represents the n umber of quarters. From this we can represent the number of dimes as twice, or 2x.

We can do the same as there are 4 more nickels than dimes and dimes is represented as 2x, we can get 2x+4

Same with the last as many quarters mneaning 3x.

Answer:

a) d = 3x

b) n = 3x + 4

c) p = 3x

Step-by-step explanation:

The first thing we have to do is understand and translate the word problem into a math equation.

Let's first start with using different variables for each denomination and later we will convert everything in terms of x which is the number of quarters.

Let
p = number of pennies
d = number of dimes
q = number of quarters

Now wherever there is a q in the equation, substitute it with x

Equation (1)     d = 3q ==> d = 3x   (substituting x for q)
Equation (2)     n = d + 4 ==> n = 3x + 4 (substituting 3x for d)
Equation (3)     p = 3q ==> p = 3x   (substituting x for q)

Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

\(\frac{(4v^{-3})^3}{3v^{-8}} =\frac{64v^{-9} }{3v^{-8} } =\frac{64}{3} v^{-9--8} =\frac{64}{3} v^{-1} = \frac{64}{3v}\)

Hope that helps!

the function will be f(x) = x³ + 2 x² - 8x.

We are given that:

The degree of the polynomial function f(x) is = 3

Roots of the function for f(x) = 0 are:

-4, 0 and 2

That is

x = -4, x = 0 and x = 2

Which can also be written as:

x + 4 = 0, x = 0 and x - 2 = 0

So, the function will be:

f(x) = (x + 4) (x) (x - 2)

f(x) = x (x² - 2 x + 4 x - 8)

f(x) = x (x² + 2 x - 8)

f(x) = x³ + 2 x² - 8x

Graph of the function is shown in the image.

Therefore, the function will be f(x) = x³ + 2 x² - 8x.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{a = - 11}}}}}\)

Step-by-step explanation:

\( \sf{4a - 2(3a + 8) = 6}\)

Distribute 2 through the parentheses

\( \longrightarrow{ \sf{4a - 6a - 16 = 6}}\)

Collect like terms

\( \longrightarrow{ \sf{ - 2a - 16 = 6}}\)

Move 16 to right hand side and change it's sign

\( \longrightarrow{ \sf{ - 2a = 6 + 16}}\)

Add the numbers: 6 and 16

\( \longrightarrow{ \sf{ - 2a = 22}}\)

Divide both sides by 2

\( \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{22}{ - 2}}} \)

Calculate

\( \longrightarrow{ \sf{a = - 11}}\)

Hope I helped !

Best regards! :D

Yes, triangle inequality theorem apply to all equilateral triangles.

The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.

A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.

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Answer:

29 oranges rounding up but the exact answer is 29.41176

Step-by-step explanation:

It would be 29.41176 if you want the answer to be exact. All you're doing is dividing 10.00 ÷ 0.34 and getting 29 oranges :)

Gina can buy 29 oranges for 10 dollars.

A decimal is represented by a dot which separates the whole par and the fractional part of a number.

According to the given question Gina visits her local farm stand to buy apples and oranges to make a fruit salad.

She has​ 10 dollars to spend and she only buys oranges and oranges are 0.34 dollars she can buy (10/0.34) oranges which is

= 29.41. But she can not buy oranges in fractions so the most no. of oranges she can buy is 29.

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To determine the probability that the fourth person will be the first customer to enter the store, we can use the geometric distribution.

The geometric distribution models the number of trials needed to achieve the first success (entering the store in this case) in a series of independent Bernoulli trials (each potential customer walking by). The probability of success in each trial is given as 0.61.

The probability that the fourth person will be the first customer to enter the store is equal to the probability of three consecutive failures (the first three people not entering the store) followed by a success (the fourth person entering the store).

The probability of failure in each trial is given by (1 - 0.61) = 0.39.

So, the probability that the fourth person will be the first customer to enter the store is calculated as follows:

P(fourth person is the first customer) = P(failure) * P(failure) * P(failure) * P(success)

= 0.39 * 0.39 * 0.39 * 0.61

≈ 0.0602

Therefore, the probability that the fourth person will be the first customer to enter the store is approximately 0.0602, or 6.02%.

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The number of bombs that should be dropped to give a 99% chance or better of completely destroying the target can be 11, 12, and 13.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of success in one strike is p = 1/2

The probability of failure will be:

q = 1/2 ​

Now, the probability of a successes P( x = a ) = ₙCᵃ ​× ( 1/2​ )ᵃ × ( 1/2 )ⁿ ⁻ ᵃ

P( x = a ) = ₙCᵃ ​ ( 1/2 )ⁿ

According to the given condition,

P( x ≥ 2 ) ≥ 0.99

= 1 − P( x < 2 ) ≥ 0.99

= 1 − P( x = 0 ) − P( x = 1 ) ≥ 0.99

= 1 − 0.99 ≥ ( 1 + n)/2ⁿ ​

= 2ⁿ ≥ 100 + 100n

When n = 10, 2ⁿ < 100 + 100n

For n = 11, 12, 13, 2ⁿ > 100 + 100n

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

224

Step-by-step explanation:

Hello!

To find f(-7) you simply plug the value, -7, into the function.

This will get you:

f(-7) = 4(-7)^2 - 4(-7)

Remember that the square of a negative number is a positive! Also, remember to use the order of operations (PEMDAS)!

This will get you:

f(-7) = 4(49) - 4(-7)

f(-7) = 196 - (-28)

f(-7) = 224

Hope this helps!

(b) An equilateral triangle has 3-fold rotational symmetry, while (d) A cube has 4-fold rotational symmetry.

Rotational symmetry refers to the property of an object where it looks the same after it has been rotated a certain number of degrees around a central point. The number of times an object looks the same after a full rotation is called its order of rotational symmetry.
(a) An isosceles triangle has no rotational symmetry because it will not look the same after any degree of rotation around its center.

An isosceles triangle has no rotational symmetry. This is because it will not look the same after any degree of rotation around its center. For example, if you rotate an isosceles triangle by 180 degrees, it will be upside down and look completely different.
An equilateral triangle has 3-fold rotational symmetry. This means that it will look the same after being rotated 120 degrees and 240 degrees around its center. To see this, imagine drawing an equilateral triangle and marking its center. If you rotate the triangle 120 degrees around the center, each vertex will be in the same position as before, and the triangle will look the same. Similarly, if you rotate it 240 degrees, it will look the same as the original triangle.

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Answer:

B,C,D

Step-by-step explanation:

becuae they are all on different x coordinates they y coordinate dont matter that much

The graphs of ordered pairs represent functions are B, C and D.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

As, we know the function have a property that No one input value have two output value.

That means that the input value have only one output.

The first graph have two output share same input.

The graph B, C and D have one output for one input value.

and, the last graph have two output share same input.

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Answer:

1

Step-by-step explanation:

Answer: 6,8

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

The answer is simple; the number of non-red marbles over the number of total marbles.

The largest share of national health expenditures is typically attributed to D. personal health care.

What is personal health care?

Personal health care refers to the direct provision of medical goods and services to individuals, including services such as hospital care, physician services, prescription drugs, and other medical supplies. These expenses typically make up the majority of national health expenditures in many countries, including the United States.

Examples of Personal Health Care Services: Personal health care expenditures include costs associated with hospital care (inpatient and outpatient), physician and specialist services, laboratory tests, prescription drugs, medical devices, home health care, nursing home care, and other healthcare services utilized by individuals.

Factors Contributing to Personal Health Care Expenses: Several factors contribute to the high share of national health expenditures attributed to personal health care. These include the increasing prevalence of chronic diseases, advances in medical technology, rising healthcare utilization, and an aging population requiring more healthcare services.

Private Health Insurance: While personal health care expenditures primarily refer to direct payments made by individuals or on their behalf, a significant portion of these costs is covered by private health insurance. Private insurance plans help individuals offset the financial burden of healthcare expenses by pooling risks and providing coverage for various medical services.

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Elaine's mean grade is 91.95.

To find Elaine's mean grade, we first need to calculate her overall grade based on the weights of each assignment. The quizzes each count for 15%, so their combined weight is 30% (15% x 2 quizzes). The final exam counts for 55%.

To calculate Elaine's overall grade, we need to multiply each assignment grade by its weight and add them together, then divide by the total weight.

So, her overall grade would be:

((67 x 0.15) + (64 x 0.15) + (87 x 0.30) + (84 x 0.55)) / 1

Simplifying this expression, we get:

(10.05 + 9.60 + 26.10 + 46.20) / 1

= 91.95

Therefore, Elaine's mean grade is 91.95.

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