What is the equation in vertex form of a parabola with a vertex of (–3, 4) that passes through the point (1, –4)

Answer:

the total area under the normal distribution is 0.0684.

Step-by-step explanation:

We can use a standard normal distribution table or a calculator to find the areas S₁ and S₂.

Using a standard normal distribution table or calculator, we find:

S₁ = 0.0158

S₂ = 0.0526

To find the total area S₁ + S₂, we simply add these two values:

S₁ + S₂ = 0.0158 + 0.0526 = 0.0684

Therefore, the total area under the normal distribution is 0.0684.

The angle x to the nearest degree is 47°.

To find the value of the angle to the nearest degree, we can use the inverse tangent function, which relates the opposite and adjacent sides of a right triangle to the angle opposite the opposite side. Specifically, we can use the formula:

tan(A) = opposite/adjacent where A is the value of angle.

Here, "opposite" is the height of the triangle (11) and "adjacent" is the base of the triangle (10).

We can solve for x by taking the inverse tangent (or arctangent) of both sides of the equation:

[tex]$ \rm x = tan^{-1} \left( \frac{opposite }{adjacent}\right)[/tex]

[tex]$ \rm x = tan^{-1} \left( \frac{11}{10}\right)[/tex]

Using a calculator, we can evaluate this expression to find

x ≈ 47.34 °

To round this to the nearest degree, we can look at the decimal part of the answer (0.34) and see that it is closer to 0.5 than 0. Therefore, we can round up to the nearest degree x ≈ 47 degrees

So, the angle x to the nearest degree is 47 degrees.

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Complete question:

Answer:

64 in^2.

Step-by-step explanation:

The surface consists of 4 congruent triangles and a square base.

Area of 1 triangle = 1/2 * 4*6  = 12.

Area of the base = 4*4 = 16.

So the required surface area

= 4*12 + 16

= 64 in^2.

Answer:

9 × ( 9 + 5 )

Hope this helps!

Step-by-step explanation:

The GCF of 81 and 45 is 9.

This is the answer to your problem

As per the given measurement, you would need to burn an extra 500 calories every day in order to lose 9 pounds in 63 days, assuming that the rest of your diet remains constant.

We know that in order to lose 1 pound of body weight, you need to burn an extra 3500 calories. Therefore, to lose 9 pounds, you would need to burn an extra 31,500 calories

=> (9 pounds x 3500 calories per pound).

If you divide this number by the number of days in which you want to achieve this goal, you'll find the amount of calories you need to burn each day. In this case, it would be:

31,500 calories / 63 days = 500 calories per day

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The correct statements are:

B. Jessie’s pyramid has a volume of 525 in^3. (Using the formula for the volume of a pyramid, V = (1/3) * base area * height, we get V = (1/3) * 15^2 * 7 = 525 in^3.)

D. Carl’s pyramid is 3.6 times larger than Jessie’s. (Using the formula for the volume of a square pyramid, V = (1/3) * base area * height, we can find the base side length of Carl's pyramid: base side length = sqrt((3*1890)/(7*15^2)) ≈ 18.46 inches. Therefore, the ratio of volumes is (18.46/15)^2 * (7/7) ≈ 3.6.)

Answer:The correct statements are:

B. Jessie’s pyramid has a volume of 525 in^3. (Using the formula for the volume of a pyramid, V = (1/3) * base area * height, we get V = (1/3) * 15^2 * 7 = 525 in^3.)

D. Carl’s pyramid is 3.6 times larger than Jessie’s. (Using the formula for the volume of a square pyramid, V = (1/3) * base area * height, we can find the base side length of Carl's pyramid: base side length = sqrt((3*1890)/(7*15^2)) ≈ 18.46 inches. Therefore, the ratio of volumes is (18.46/15)^2 * (7/7) ≈ 3.6.)

Step-by-step explanation:

The quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:

[tex]$x^2 + 12x - 17 = 0$[/tex].

What is quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means it involves an unknown variable (usually denoted as x) that is raised to the power of 2. The general form of a quadratic equation is given by:

a[tex]x^{2}[/tex] + bx + c = 0

where a, b, and c are constants, and a is not equal to 0.

The quadratic equation that could be solved to find any solutions to the system of equations

[tex]$y = -5x + 6$[/tex]

[tex]$y = x^2 + 7x - 11$[/tex]

is given by:

[tex]$x^2 + 12x - 17 = 0$[/tex]

Therefore, the quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:

[tex]$x^2 + 12x - 17 = 0$[/tex]

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The hypothesis for the given scenario can be written as follows:

Null hypothesis

H_0: μ = 7.2

Alternative hypothesis

H_1: μ ≠ 7.2

Here, μ = Population mean

The mean pressure produced by the valve is not 7.2 lbs/square inch.

The given level of significance (α) = 0.05

The given population variance is known to be 1.

Need to determine if there is sufficient evidence to show that the valve does not perform to the given specifications if the valve was designed to produce a mean pressure of 7.2 lbs/square inch. That is, whether to reject or accept the null hypothesis with the given level of significance (α) = 0.05.

The sample mean pressure of 190 engines tested was 7.3 lbs/square inch. Mean pressure (μ) = 7.3 lbs/square inch, σ² = Variance = 1, n = Number of observations = 190

Significance level (α) = 0.05

Test Statistic: Z = (x - μ) / (σ / √n)

where x = Sample mean

The formula for the test statistic can be written as:

Z = (7.3 - 7.2) / (1 / √190)Z = 4.3588 (approx.)The calculated value of Z = 4.3588 is greater than the Z critical value at 0.05 level of significance.

Hence, there is sufficient evidence to reject the null hypothesis H_0. Therefore, we can conclude that the valve does not perform to the given specifications. The mean pressure produced by the valve is not 7.2 lbs/square inch.

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Answer: length is 33ft

Step-by-step explanation:

Perimeter = length x2 + width x2 (add all sides of a rectangle)

width = 15ft

15 x 2 = 30 ft

86ft - 30 ft = 66 ft

66/2 = length of 1 side = 33 ft

192 ways that Fred can dress for the week

Outfit Choices: 7 Days

Angel

Fred is looking to pick out his clothes for the next 7 days. He has two different pairs of pants and

two different shirts. Each day he needs to wear a different outfit than what he wore the day before.

However, he has already chosen his outfit for Friday due to a formal occasion. How many ways can he

dress for the week?

Since Fred has already chosen his outfit for Friday, he only needs to choose 6 outfits for the remaining days of the week (Saturday through Thursday).

For each day, he has 2 choices for pants and 2 choices for shirts. So there are 2 × 2 = 4 possible outfits for each day.

To make sure he wears a different outfit each day, Fred needs to choose a different outfit from the previous day's outfit. For Saturday, he has 4 choices. For Sunday, he has 3 choices (since he cannot wear Saturday's outfit), and so on, until Thursday, for which he has only 1 choice.

Answer:

y² + 6y + 9.

It can be expressed into two binomials like this.

Answer:

(y + 3)(y + 3)

Using (a+b)² = (a+b)(a+b)

To estimate the number of rubber balls in the whole basket, we can multiply this proportion by the total number of balls. Therefore, We can estimate that there are about 21 rubber balls in the basket.

An average proportion is the sum of a set of proportions divided by the number of proportions.

It represents the average or typical value of the proportions in the set, and can be used to estimate the overall proportion or percentage of a larger population.

To estimate how many of the balls in the basket are rubber, we can use the proportion of rubber balls that were drawn in each class to find the average proportion of rubber balls across all four classes.

We can then use this average proportion to estimate the number of rubber balls in the whole basket.

The total number of balls drawn from the basket is:

(2 + 8) + (4 + 6) + 2 x (3 + 7) = 40

The total number of rubber balls drawn is:

2 + 4 + 2 x 3 = 12

The proportion of rubber balls drawn in each class is:

Class 1: 2/10 = 0.2

Class 2: 4/10 = 0.4

Class 3: 3/10 = 0.3

Class 4: 3/10 = 0.3

The average proportion of rubber balls across all four classes is:

(0.2 + 0.4 + 0.3 + 0.3) / 4 = 0.3

Therefore, we can estimate that approximately 30% of the balls in the basket are rubber. To estimate the number of rubber balls in the whole basket, we can multiply this proportion by the total number of balls:

Number of rubber balls = 0.3 x 70 = 21.

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We can conclude by answering the provided question that Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

In mathematics, a function appears to be a connection between two groups of numbers in which each member of the first set (known as the domain) correlates to a specific member of the second set (called the range). In other terms, a function takes input from one set and generates output from another. The variable x has frequently been used to represent inputs, and the variable y has been used to represent outcomes. A formula or a grid can be used to describe a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x gives a unique value of y.

We can deduce from the provided function:

g(x) = 0 when x = 0.

For 0 x 1, g(x) = x2.

g(x) = 2 - x for 1 x 2.

g(x) = 0 when x > 2.

So, to draw the graph of g(x), we can join the points (x, g(x)) for various values of x within the specified intervals.

Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

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Answer:

☆ -10 ☆ is your correct answer!

Answer: A: $2374.56

there

Step-by-step explanation:

FICA taxes is the Social Security and the Medicare added together

So you add 1924.48+450.08 and you get 2374.56

For a continuous function, if the second derivative at the critical points is negative, then it not necessarily mean that it is quasi-concave.

A "continuous-function" is defined as a function in which small changes in the input result in small changes in the output, without any abrupt jumps or discontinuities.

A function is termed as "quasi-concave" if its upper contour sets are convex.

A function is termed as "quasi-convex" if its lower contour sets are convex.

The "Quasi-concavity" is a weaker condition than concavity, so it does not exhibit in a condition on the sign of "second-derivative".

Therefore, if a continuous function has a negative second derivative at its critical points, it does not necessarily mean that it is quasi-concave.

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Let "e" be the elevation of the submarine and "t" be the time taken to descend.

Then, the equation representing the relationship between the submarine elevation and time is:

e = -105t + 2100

where the coefficient of "t" (-105) represents the rate of descent of the submarine, and the constant term (2100) represents the initial elevation of the submarine.

Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

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The pairs of lines are classified as: perpendicular, parallel, neither, neither.

The slopes of the first pair of lines differ, making them neither parallel nor perpendicular. The slopes of the first and second lines are 1/2 and -2, respectively.

The second set of lines is perpendicular because the slopes of the first line, which is -3, and the second line, which is 1/3, are the opposites of each other.

The third set of lines have varying slopes and are neither equal nor perpendicular. The slopes of the two lines are -2/3 for the first line and 6/4 for the second, which reduces to 3/2.

To classify each pair of lines as parallel, perpendicular, or neither, we need to compare their slopes.

2y = x and y = -2x + 6

The first equation can be written in slope-intercept form as y = (1/2)x, which means its slope is 1/2. The second equation can be written in slope-intercept form as y = -2x + 6, which means its slope is -2. Since the slopes are negative reciprocals of each other, these lines are perpendicular.

y + 3x = 1 and 2y = -6(x - 1)

The first equation can be written in slope-intercept form as y = -3x + 1, which means its slope is -3. The second equation can be written in slope-intercept form as y = -3x + 3, which means its slope is also -3. Since the slopes are the same, these lines are parallel.

3y + 2x = -3 and 4y = 6x + 12

The first equation can be written in slope-intercept form as y = (-2/3)x - 1, which means its slope is -2/3. The second equation can be written in slope-intercept form as y = (3/2)x + 3, which means its slope is 3/2. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

y + 2 = 5x and 5y - x = -2

The first equation can be written in slope-intercept form as y = 5x - 2, which means its slope is 5. The second equation can be written in slope-intercept form as y = (1/5)x - 2/5, which means its slope is 1/5. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

Therefore, the pairs of lines are classified as follows:

perpendicular

parallel

neither

neither

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The measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

The upper base angles m∠DAB and m∠ADC are equal, and angles m∠ADC and m∠DCB are supplementary, so we shall calculate for the angle m∠DAB by first evaluating for angle m∠ADC as follows:

m∠ADC + m∠DCB = 180° {opposite angles are supplementary}

m∠ADC + 105° = 180°

m∠ADC = 180° - 105° {subtract 105° from both sides}

m∠ADC = 75°

m∠ADC = m∠DAB = 75°

Therefore, the measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.

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(9x+7=10x-10)

All terms are shifted to the left:

(9x+7-(10x-10))=0

Parentheses are used to compute terms: +(9x+7-(10x-10)), so:

9x+7-(10x-10)

the Function Domain determination

9x-(10x-10)

+7

We eliminate parenthesis.

9x-10x+10+7

All the numbers and variables are added together.

-

1x+17

Returning to the equation

+(-1x+17)

We eliminate parenthesis.

-1x+17=0

We shift every term that contains x to the left and every other term to the right.

-x=-17 \sx=-17/-1 \sx=+17

How can you determine an equation's degree?

The degree of a term in the polynomial expression is expressed as a + b if a and b are the exponents of the many variables in a term.

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Answer:

the answer is Undefined

Step-by-step explanation:

therefore the value of x is basically 0

I do indeed hope this helps

Answer:

a. y = 6.5x + 3.99

b. y = 10.49x

Step-by-step explanation:

a.

total cost = charge per shirt + flat rate of shipping

y = 6.5x + 3.99

b.

total cost = charge per shirt + shipping charge per shirt

y = 6.5x + 3.99x

y = 10.49x

If the shipping charge applies to every shirt, then the total cost is the cost of the shirts (6.5x) plus the cost of shipping multiplied by the number of shirts (3.99x)

Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5).

A translation in mathematics is a transformation of such a curve or a this double object that entails moving the curve or item from point to point along its graph. We have different terms to express this kind of alteration according to the nature of translation.

Initial coordinates of Retention Pond 1:

(-8,8) , (-8, 3), (-4, 3) and (-4, 8)

After the translation of 8 units to the right. Add 8 to each x-coordinates.

After the translation of  13 units down. subtract 13 to each y-coordinates.

(-8,8)  = (-8 + 8,8 - 13)  = (0, -5)

(-8, 3) =  (-8 + 8, 3 - 13) = (0, -10)

(-4, 3) = (-4 + 8, 3 - 13) = (4, -10)

(-4, 8) = (-4 + 8, 8 - 13)  = (4, -5)

Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5). There will be no change in the area.

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Answer:

Width = 10

Step-by-step explanation:

let length = X

width = 3X - 2

Area = length x width

40 = X x (3X - 2)

40 = 3X^2 - 2X

therefore 3X^2 - 2x - 40 = 0

3x^2 + 10x - 12x - 40 = 0

x(3x + 10) - 4(3x + 10) = 0

(x - 4) (3x + 10) = 0

(x - 4) = 0

x = 4

(3x + 10) = 0

3x = - 10

x = -10/3

Since the lenght can't be negative, we'll work with x = 4

Therefore the width = 3x - 2

Width = 3(4) -2

Width = 12 - 2

Width = 10

Answer:

Solution for What is 0.56 percent of 72:

0.56 percent *72 =

(0.56*72):100 =

40.32:100 = 0.4032

Now we have: 0.56 percent of 72 = 0.4032

Question: What is 0.56 percent of 72?

Percentage solution with steps:

Step 1: Our output value is 72.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 72=100\%

Step 4: Similarly, x=0.56%.

Step 5: This results in a pair of simple equations

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%)

Step 7: Again, the reciprocal of both sides gives

I hope this helped! A brainilist is appreciated and helpful! <333

X = 1 , 4 are the value of x in logarithm.

A logarithm is defined simply?

A logarithm is a mathematical operation that raises a number to a given power in order to produce another number (see Section 3 of this Math Review for more about exponents).

                                    As an example, the logarithm of 100 in base ten is 2, since ten times two equals 100: log 100 = 2, since 102 = 100. The four most prevalent kinds of logarithms are common logarithms with a base of 10, natural logarithms with a base of e 2.71828, binary logarithms with a base of 2, and logarithms with a base of 2.

2log₃(6x) - log₃(4x) - 2log₃(x + 2) = 0

log₃(9x/(x+ 2)²) = 0

 exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then

         logb(x) = y  equivalent to [tex]b^{y}[/tex] = x

   3⁰ =  9x/(x + 2)²

 9x =     3⁰ (x + 2)²

   9x = x² + 4x + 4

     -x² + 5x = 4

 Factor x out of -x²

    x(-x) + x. 5 = 4

      x(-x + 5) = 4

    -x² + 5x - 4 = 0

 - ( x - 4) ( x - 1) = 0

     x = 4 , 1

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