Which of the following are equivalent to the statement “the price decreased by 1/3”?

Choose ALL the correct answers:

(A)The price doubled

(B)The price is 150% of the price before.

(C)The price was reduced by a quarter

(D)The price is half of what it was before

(E)The price is now 1.5 times greater than what it was before

(F)The price is now 66 2/3% of what it was before

(G)The price now is 200% of what it was before.

(H)The price is 75% of what it was before

Answer:

a. DE = 15 cm

b. AB = 6 cm

Step-by-step explanation: Since these triangles are similar, you can find a factor that represents the corresponding side of one triangle to another. AC and CE are similar and both are given. AC is 1/3 of CE and CE is 3 time AC so those are the factors. To solve for DE we know that the length will be three times its corresponding side BC and therefore will be 15 cm. AB is one third of CD and will therefore be 18/3 which is 6 cm.

Answer:

5.8

Step-by-step explanation:

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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the expression is

so the correct answer is d = -16

Point ( 0 , -27 ) on the line and  ( -9 , 0 ) are not on the line

Given :

Madison is reeling in her string at a steady rate the linear equation 3y - 9x = -81 can be used to find y the number of feet of kite string she still needs to reel in after x seconds .

Points ( 0 , -27 )

when x = 0

3y - 9 * 0 = -81

3y - 0 = -81

3y = -81

y = -81 / 3

y = -27

so point ( 0 , -27 ) on the line .

when y = 0

3 * 0 - 9x = -81

0 - 9x = -81

-9x = -81

x = 81/9

x = 9

so ( -9 , 0 ) are not on the line

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Answer:

G(1) = -2

Step-by-step explanation:

for G(1) replace x with 1

G(1)=1-3

subtract

1-3 = -2

so G(1) = -2

We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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Answer:

To calculate how many packages Marcella has wrapped, you need to first calculate how many packages each roll of wrapping paper can be used for. Since Marcella uses 1/2 of a roll of wrapping paper for every 3 packages, it follows that she can wrap 3 packages for every 1/2 roll of wrapping paper. Therefore, 2 1/2 rolls of wrapping paper can be used to wrap 15 packages.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{5.68 \: dollars}}}}}\)

Step-by-step explanation:

Total money that Hannah had = $ 19.27

Total money that Riley had = $ 13.59

Finding the more money that Hannah have :

Total money that Hannah had - Total money that Riley had

\( \longrightarrow{ \sf{19.27 - 13.59 }}\)

\( \longrightarrow{ \sf{5.68 \: dollars}}\)

Hope I helped!

Best regards! :D

All we need to do is subtract.

19.27 - 13.59 = $5.68

Therefore, Hannah as $5.68 more than Riley.

Best of Luck!

The first two non-zero terms of f'(x) are 12kx^(k-1) and 12(k-1)x^(k-2), and the last two non-zero terms are 12x and 12.

To find the derivative of f(x), we need to differentiate each term of the given function f(x) = 12x^k/k!. The derivative of x^k with respect to x is kx^(k-1), and the derivative of a constant (12 in this case) is zero. Additionally, the derivative of k! (k factorial) is zero, as it is a constant.

Therefore, the derivative of f(x) is obtained by differentiating each term separately. The first term in f'(x) is obtained by differentiating 12x^k/k!, which gives us 12kx^(k-1). The second term is obtained by differentiating the constant term 12x^(k-1)/k!, resulting in 12(k-1)x^(k-2).

The last two non-zero terms of f'(x) are obtained by differentiating the last two terms of f(x). The derivative of 12x with respect to x is 12, and the derivative of 12 (constant term) is zero.

In summary, the first two non-zero terms of f'(x) are 12kx^(k-1) and 12(k-1)x^(k-2), and the last two non-zero terms are 12x and 12.

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Answer:

x = 4 or x = -1

Step-by-step explanation:

2x^2 - 8x + 6 =0

divide by 2 we get  : x^2 -4x +3 = 0

(x -4) (x+1)

x = 4 or x = -1

PART A: component form of the vector is:

u = <3, 3√3>

v = <2√2, -2√2>

w = <-6√3, 6>

-7(u • v) = 42(√6 - √2)

PART B:  u and w are orthogonal

The component form of a vector is <x, y>.

PART A:

u = 6(cos 60°i + sin60°j)

x = 6(cos 60) = 6 * 1/2 = 3

y = 6(sin 60) = 6 * (√3)/2 = 3√3

In component form, u = <3, 3√3>

v = 4(cos 315°i + sin315°j)

x = 4(cos 315°) = 4 * (√2)/2 = 2√2

y = 4(sin 315°) = 4 * (-√2)/2 = -2√2

v = <2√2, -2√2>

w = −12(cos 330°i + sin330°j)

x = -12(cos 330°) = -12 * (-1/2) = -6√3

y = -12(sin 330°) = -12 * (√3)/2 = 6

w = <-6√3, 6>

The dot product of two vectors is given by:

A•B = A\(_{x}\)B\(_{x}\) + A\(_{y}\)B\(_{y}\)

−7(u • v) = -7 * [(3 * 2√2) + (3√3 * -2√2)]

            = -7 * [6√2 - 6√6]

           =  42(√6 - √2)

Part B:

The vectors will be parallel if the dot product is equal to the product of the magnitudes which means the angle between the vectors is 0 or 180.

The vectors will be orthogonal if the dot product = 0. This means the angle between them = 90.

The dot product of the vectors (u) and (w) will be as follows:

u = <3, 3√3>

w = <-6√3, 6>

u • w = (3 * -6√3) + (3√3 * 6)

        = -18√3 + 18√3

        = 0

Since the result of the dot product = 0. The vectors (u) and (w) are orthogonal.

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Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the medical researcher should increase the sample size.

This will provide a more precise estimate of the mean birth weight of babies born to women over the age of 40.

Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the researcher should increase the sample size.

The larger the sample size, the smaller the margin of error, which means that the estimated mean birth weight of all babies born to women over the age of 40 will be more precise.
Redoing the study and choosing a different sample of size 100 will not necessarily reduce the margin of error, as the variability in the sample may be the same.

To achieve a smaller margin of error, the researcher needs to increase the sample size.
With a larger sample size, the researcher will have a more representative sample of the population, which will lead to a more accurate estimate of the mean birth weight of all babies born to women over the age of 40.

However, the larger sample size may require more resources and time to collect the data.

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Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:v = y(1-n)dv/dx = (1-n)y-n dy/dxso dy

Step-by-step explanation:

Reason: It's the coefficient to the left of the input variable.

The system of inequalities that represents the scenario is:

x^2 - 2y ≥ 6,000

2x + 5y ≤ 2,000


To represent the company's goal of maintaining a stock value of at least $6,000, we use the inequality x^2 - 2y ≥ 6,000. This means that the value of x^2 - 2y must be greater than or equal to $6,000 in order for the company to meet their goal.

To represent the company's goal of keeping purchases below $2,000, we use the inequality 2x + 5y ≤ 2,000. This means that the value of 2x + 5y must be less than or equal to $2,000 in order for the company to meet their goal.

Therefore, the system of inequalities that represents the scenario is:

x^2 - 2y ≥ 6,000

2x + 5y ≤ 2,000

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Answer:

7850 mi

Step-by-step explanation:

Area of a circle is:

A = (pi)r²

A = (3.14) (50²)

A = (3.14) (2500)

A = 7850 square miles

You need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

First, 5% of the total cost for four years.

= 0.05 x ($14,895.00/yr x 4 years)

= 0.05 x $59,580.00

= $2,979.00

Second, Divide the total amount you need to pay over four years by the number of years.

= $2,979.00 / 4

= $744.75

Therefore, you need to pay $744.75 for each year of attending college.

Now, the total contribution goal.

= Amount to pay each year x 4 years

= $744.75 x 4

= $2,979.00

and, Monthly savings required

= Total contribution goal / 48 months

= $2,979.00 / 48

= $62.06

Therefore, you need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

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Answer:  Choice B

\(\text{As } x \to \infty, \ f(x) \to \infty\)  and \(\text{As } x \to -\infty, \ f(x) \to \infty\)

==========================================================

Explanation:

Assuming that the only roots are x = -3 and x = 2, as shown by the table, then notice how f(x) > 0 at the very right hand side of the table. This indicates that f(x) will remain positive for this tail end. If f(x) were to become negative, then there would have to be another root somewhere beyond x = 2 (but that contradicts the assumption made at the top of the paragraph).

This allows us to say \(\text{As } x \to \infty, \ f(x) \to \infty\)

In other words, as x gets bigger, so does y. Both head to positive infinity together. We can informally describe this end behavior as "rises to the right".

----------------------

For the left side of the table, we also have positive f(x) values to the left of the root. So we see that f(x) > 0 as x heads off in the negative infinity direction.

We would then say \(\text{As } x \to -\infty, \ f(x) \to \infty\)

Regardless of what direction x goes (positive or negative infinity), the y = f(x) values are heading off to positive infinity. Informally, we could say "rises to the left".

Both endpoints rise together to positive infinity. Think of a parabolic curve that opens upward as one example.

All of this points to choice B as our final answer. Choice B can be rephrased as \(\text{As } x \to \infty \text{ or } x \to -\infty, \text{ then } \ f(x) \to \infty\)

Firstly, we calculate the number of products whose prices are perfect cubes. Then, using these perfect cube prices, we determine the number of pairs whose sum also forms a perfect cube.

In order to count the number of pairs (i, i) such that the sum of their prices is a perfect cube, we need to follow a two-step process.

Step 1: Identifying Perfect Cube Prices

We begin by determining the number of products with prices that are perfect cubes. For each product's price, we take its cube root and check if the result is an integer. If it is, we increment a counter variable to keep track of the number of perfect cube prices.

Step 2: Counting Pairs with Perfect Cube Sum

Next, we utilize the perfect cube prices obtained in the previous step to count the number of pairs whose sum is also a perfect cube. We iterate through the list of perfect cube prices and calculate the sum of each pair (i, i). If the sum is a perfect cube, we increment a separate counter variable to track the number of qualifying pairs.

Finally, we return the count of qualifying pairs as the answer. This approach ensures that we consider only the pairs (i, i) where the sum of their prices satisfies the given conditions, allowing us to determine the number of pairs eligible for the 50% discount during Amazon Prime Day.

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Hello there!

Point-Slope Form:

y-y₁=m(x-x₁)

We are given m (the slope) and the point (5, 8)

y-8=3(x-5)

And that's our equation in point-slope form. Hope it helps! :)

\(GraceRosalia\)

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

A =153.86 cm^2

Step-by-step explanation:

The diameter is 14 so the radius is d/2 = 14/2 = 7

A = pi r^2

A = (3.14) (7)^2

A =153.86 cm^2

Answer:

Step-by-step explanation:

First you take the diameter and cut it in half to find the radius. 14/2 = 7

Next you times the radius to the power of 2. 7^2= 49

Then you times your answer by 3.14. 49*3.14 = 153.86

153.86cm² is your answer

Using ratio and proportion, Louie is correct.

Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.

From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).

If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.

FP : PG = 4 : 1

FP/PG = 4/1 = 4

x-coordinate of P

(4 - x)/(x - -6) = 4

(4 - x) = 4(x + 6)

4 - x = 4x + 24

-5x = 20

x = -4

y-coordinate of P

(8 - y)/(y - -7) = 4

(8 - y) = 4(y + 7)

8 - y = 4y + 28

-5y = 20

y = -4

Hence, the coordinates of Point P is (-4, -4).

Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.

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The best prediction is

(C) x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞.

An interval is a set of real numbers between two given numbers called the endpoints of the interval.

Given:

x  f(x)

-4  18

-3  9

-2  6

-1  3

0  0

1  -3

2  -6

3  -9

4  -18

As, from the table x increases, the value of f(x) decreases

i.e. Over time, when x → ∞, f(x) → –∞

and then x decrease, the value of f(x) increases

when x → –∞, f(x) → ∞.

Hence, best predicts the end behavior of the graph of f(x) is x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞.

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Answer:

its C

Step-by-step explanation:

Dilation and rotation transformation produces shapes that are not congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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Subtract sin (8x − 10) from both sides of the equation.

cos (6x − 12) − sin (8x − 10) = 0

Answer:

It doesn't exist

Step-by-step explanation:

since :

cos (90° – x) = sin x

cos(x) = sin(pi/2 - x)

then

cos(6x-12) =! sin(8x-10)

since (8x-10) =! (pi/2- 6+12)

then this identity of cos(6x-12) = sin(8x-10) doesn't exist

Answer:

I'm not understanding the second part. Can you elaborate more in the comments?

But it would cost $21

Answer:

$21

Step-by-step explanation:

You have to use ratios

\(\frac{12}{3} =\frac{84}{x} \\\\12x=252\\x=21\)

It would cost $21 to make 84 copies

The expression 4a - b evaluates to -22. To get the answer, substitute the values of a, b, and perform the arithmetic: (4 * -5) - 2 = -22.

To evaluate the expression 4a - b, you need to substitute the given values of a, b, and c into the expression and perform the calculation.

Given that a = -5 and b = 2, you can substitute these values into the expression:
4a - b = 4(-5) - 2

Now, you can simplify the expression by performing the multiplication and subtraction:
= -20 - 2
= -22
Therefore, when you evaluate the expression 4a - b with the given values of a = -5 and b = 2, you get the result of -22.

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when a = -5 and b = 2, the expression 4a - b evaluates to -22.

To evaluate the expression 4a - b, we substitute the given values of a = -5 and b = 2 into the expression.

Step 1: Substitute the value of a = -5 into the expression.
4(-5) - b

Step 2: Simplify the expression.
-20 - b

Step 3: Substitute the value of b = 2 into the expression.
-20 - 2

Step 4: Simplify the expression.
-22

Therefore, when a = -5 and b = 2, the expression 4a - b evaluates to -22.

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