Kosey needs to get 80% of his
questions correct on his math test
to get a B for the quarter. If his
test has 60 questions, how many
questions will he need to get right?

(a) The limit lim f(x) as x approaches -2 = -12 + m. B) The limit  lim f(x) as x approaches ∞ = 0 , To find the limit of f(x) as x approaches -2, we substitute -2 into the function f(x) = 6x + m.  c) value of m that satisfies the condition is m = 38.

So, lim f(x) as x approaches -2 = 6(-2) + m = -12 + m.
(b) To find the limit of f(x) as x approaches ∞ (infinity), we need to consider the highest power of x in the function.
Since the highest power of x is x2, we divide every term in the function by x2 to find the limit.

So, lim f(x) as x approaches ∞ = lim (6x/x2) + (m/x^2) + (2 - 7x2)/x^2.
As x approaches ∞, the terms (6x/x2) and (m/x2) both approach 0, and the term (2 - 7x2)/x2 approaches 0 as well.
Therefore, lim f(x) as x approaches ∞ = 0 + 0 + 0 = 0.

(c) To find the values of m such that the limit of f(x) as x approaches 2 exists, we need to find the values of m for which the left-hand limit and the right-hand limit are equal.  Let's first find the left-hand limit, lim f(x) as x approaches 2- (from the left side).  Substituting x = 2 into the function f(x) = 6x + m, we have lim f(x) as x approaches 2- = 6(2) + m = 12 + m.

Now let's find the right-hand limit, lim f(x) as x approaches 2+ (from the right side). Substituting x = 2 into the function f(x) = 2 - 7x2 + 2m, we have lim f(x) as x approaches 2+ = 2 - 7(2)2 + 2m = 2 - 28 +2m = -26 + 2m.

To find the values of m such that the left-hand limit equals the right-hand limit, we equate the expressions:
12 + m = -26 + 2m. Solving this equation for m, we have m = 38. Therefore, the value of m that satisfies the condition is m = 38.

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keeping in mind that an absolute value expression is really a duet in disguise, namely there's positive and negative version of it, Check the picture below.

\(\pm (3x+12)~~ = ~~105 \\\\[-0.35em] ~\dotfill\\\\ +(3x+12)~~ = ~~105\implies 3x=93\implies x=\cfrac{93}{3}\implies \boxed{x=31} \\\\[-0.35em] ~\dotfill\\\\ -(3x+12)~~ = ~~105\implies 3x+12=-105\implies 3x=-117 \\\\\\ x=\cfrac{-117}{3}\implies \boxed{x=-39}\)

Answer:

x = 26

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is half the length of the third side, thus

x + 9 = \(\frac{1}{2}\)(3x - 8) ( multiply both sides by 2 to clear the fraction )

2(x + 9) = 3x - 8

2x + 18 = 3x - 8 ( subtract 2x from both sides )

18 = x - 8 ( add 8 to both sides )

26 = x

In monthly sales would mr. gonzalez need to have $100000

Mr. Gonzalez earns his living as a salary plus commission employee, then his annual earnings can be represented by

Monthly earnings=a+bx

Where a =his annual salary (fixed),

b = the percentage of sales commission and

X =represents the volume of sales made each year.

Therefore When  Mr. Gonzalez annual salary is $18,000 and makes a commission of 4%, his annual sales that will enable him earn an annual salary of $60,000 will be equal to

$60000 = $18000 + 0.04X

$60000 - $18000 = 0.04X

$48000 = 0.04X

0.04X = $1200000

X = $48000/0.04=12000000

X=$12000000

Therefore, his monthly sales is given by his  earnings divided evenly each month is equal to

$1200000/12=$100000

So the option c is correct.

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Answer:c

Step-by-step explanation:

quick clarification on "point E to line FH", well, point E is just a point, line FH goes to infinity both ways, so in essence how many distances are there? well, infinite many.

now, if the question is "distance closest from E to FH?", then there's only one choice, the closest distance to FH will be the perpendicular distance from E and that'd be the distance from E to G

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ E(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad G(\stackrel{x_2}{1}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ EG=\sqrt{(~~1 - (-4)~~)^2 + (~~2 - (-3)~~)^2} \implies EG=\sqrt{(1 +4)^2 + (2 +3)^2} \\\\\\ EG=\sqrt{( 5 )^2 + ( 5 )^2} \implies EG=\sqrt{ 25 + 25 } \implies EG=\sqrt{ 50 }\implies EG\approx 7.07\)

Answer:

Vertical: 2 units down

Horizontal: 1 unit left

Step-by-step explanation:

X +/- numbers: means it will go up or down

If its parentheses then it is the opposite

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

\(\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}\)

\(\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}\)

\(\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}\)

 \(\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark\)

Answer:

i don't understand 5, 8, 9, or 10.. I'm sorry...

6. A. With each one (1,2,3) the pattern increases by 3 dots each time

B. the fourth pattern would be 4 rows of 3 (look at picture below)

7. The pattern adds 2 squares, one on the left and one on the right side

Step-by-step explanation:

so... a conjecture is basically like an educated guess.. so ye :)

The distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.

Distance is the total movement of an object without any regard to direction.

To calculate the approximate reaction distance, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitiute these values into equation 1

Hence, the distance of the reaction is 11.73 m.

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Answer:

3

Step-by-step explanation:

1/2 x 3 = 3/2

Answer:

(a)

angle bisector

(b)

altitude

(c)

perpendicular bisector

Step-by-step explanation:

Answer:

-19

Step-by-step explanation:

ok so since they give you all the variables you can substitute their values

for example instead of 3xy you can write 3*(-4)y

so that is the basic idea for this problem

after substituting, the new equation is 3*(-4)*2 +5

i plan on using order of operations, or PEMDAS

3*(-4)=(-12)

(-12)*2=(-24)

-24+5=-19

so the answer is -19

hope this helps!

Answer:

B

Step-by-step explanation:

Just did it

Answer:

b

Step-by-step explanation:

Answer:

small = 35 pounds

large = 45 pounds

Step-by-step explanation:

Let x = large boxes

y = small boxes

two equations can be derived from the question

x + y = 80  equation 1

60x + 65y = 4975 equation 2

multiply equation 1 by 60

60x +60y = 4800 equation 3

subtract equation 2 from 3

5y = 175

y = 35

substitute for y in equation 1

x + 35 = 80

x = 80 - 35

x = 45

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. This will shift the triangle in the desired direction.

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. For example, if you wanted to translate the triangle with coordinates (1,2), (3,4), and (5,6) by two units to the right and two units up, you would add two to each x-coordinate and two to each y-coordinate. The new triangle would have coordinates (3,4), (5,6), and (7, 8).

1. Identify the coordinates for the triangle: (1,2), (3,4), and (5,6).

2. Decide how much you want to translate the triangle: two units to the right and two units up.

3. Add two to each x-coordinate and two to each y-coordinate: (3,4), (5,6), and (7,8).

4. The triangle is now translated two units to the right and two units up.

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a. 80% of 90 is the same as of 90 - False

b. 45% of 60 is 27 - True

c. 20% of 90 is the same as as of 90- True

d. 25 is 35% of 80 -False

a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.

b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.

c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.

Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.

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Answer:

62

Step-by-step explanation:

JL = JK + KL

5x + 2 = 3x - 1 + 27 add like terms

5x + 2 = 3x + 26

2x = 24

x = 12

JL = 12 × 5 + 2

JL = 62

The price of the TV, including tax, is $161.17 rounded to the nearest cent. To find the price of the TV including tax, we need to calculate the sale price of the TV after the 15% discount, add the sales tax, and then round to the nearest cent.

Here are the steps:

Calculate the sale price after the 15% discount:

Sale price = Original price - Discount amount

Sale price = $177.21 - (15% * $177.21)

Sale price = $150.63

Calculate the sales tax on the sale price:

Sales tax = 7% * $150.63

Sales tax = $10.54

Add the sales tax to the sale price:

Price including tax = Sale price + Sales tax

Price including tax = $150.63 + $10.54

Price including tax = $161.17

Therefore, the price of the TV, including tax, is $161.17 rounded to the nearest cent.

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The car will spend 18 minutes to cover 18 km.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s

Given that,

Time taken to travel 105 km = 1 hr 45 min = 60 min + 45 min = 105 minutes

Time taken to travel 18 km = x

Using the concept of proportion,

105 / 105 = 18 / x

Cross multiplying,

105 x = 18 × 105

x = 18

Hence the time taken to travel 18 km is 18 minutes.

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Table A does not represent a function, only table B represents a function.

To determine if a table of values represents a function, we need to check if each input value (also known as the domain) corresponds to a unique output value (also known as the range). If each input value is paired with exactly one output value, then the table of values represents a function. If any input value is paired with more than one output value, then the table of values does not represent a function.

In table A, x-value 1 is paired with two different y-values, -1 and 1. Therefore, table A does not represent a function while table B represents a function.

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the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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Answer:

(x - 8)² + (y - 10)² = 36

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Pre-Calculus

Circle Center Formula: (x - h)² + (y - k)² = r²

Step-by-step explanation:

Step 1: Define

Identify

(h, k) = (8, 10)

r = 6

Step 2: Find Equation

Answer:

0.428571429 meters

Step-by-step explanation:

Heres your answer.

The only correct statement is (E ∩ F) is the empty set

Set is a collection of thing arranged in a specific pattern.

Given the following sets

D = {x | x is a whole number}

E = {x | x is a perfect square < 36}

F = {x | x is an even number between 20 and 30}

Their equivalent elements are

D = {1, 2, 3...}

E = {1, 4, 9, 16, 25}

F = {22, 24, 26, 28}

For DnE = {1, 25}

EnF = { }

Set E contains just 5 elements and not infinite

This shows that the only correct statement is (E ∩ F) is the empty set

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Step-by-step explanation:

The law of cosine states that:

\(C^2=B^2+A^2-2AB\cos(\theta)\), where C is the side opposite of angle theta, and A and B are the adjacent sides of the angle.

In this case, A is equal to 21, and B is equal to 30 (or it could also be the other way around). That means that:

\(C^2=21^2+30^2-2\cdot21\cdot30\cos(73)\\C=\sqrt{21^2+30^2-2\cdot21\cdot30\cos(73)}=\boxed{31.186722}\) (to nearest 6 digits)

Answer:

102.61

Step-by-step explanation:

assuming that QS is the hypothesis we us the fromula like this:

\(30cos(73)\)

which gives us 8.7711511417 or we can round to 8.77

assuming that QS is the adjacent  we use:

\(\frac{30}{cos(73)}\)

which gives us 102.609108595 or rounded to 102.61

looking at both answers we can see that 102.61 would be the correct answer.

When added correctly, you will come to the answer of 959,959.

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Answer: $24.50

Step-by-step explanation:

We know that each battery  pack contains 4 batteries.

This mean that to get 28 batteries, you would need 7 packs (28/4)

7 battery packs x $3.50 = $24.50

∴, 28 batteries will cost $24.50

Answer:

The value of 6(2b-4) is 36.

Step-by-step explanation:

Given expression: 6(2b-4)

To find the value of 6(2b-4) at b=5, we need to substitute the b=5 in the expression, we get

6(2(5)-4)

= 6(10-4)

=6(6)

= 6x6=36

⇒ 6(2(5)-4)=36

Answer:

The value of 6(2b-4) when b=5 is 36.

Step-by-step explanation:

Given expression: 6(2b-4). To find the value of 6(2b-4) at b= 5, we need to substitute the b=5 in the expression, we get….Therefore, the value of 6(2b-4) is 36, when b=5.