The vertex form of the quadratic function f(x) = -6x² - 60x - 151 is
f(x)= a(x - h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?

Answer: 210

Step-by-step explanation:

3/11 is the probability of choosing an L or an S

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

The given word is SQUIRRELLED.

We need to choose single letter from the word.

We have to find the probability of choosing an L or an S

If we were to select a letter that was either an L or S from eleven letters. 1 of them being an S and 2 of them being an L.

We simply add:1+2/11

Three divided by eleven

3/11

Hence, 3/11 is the probability of choosing an L or an S

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STEP ONE: Get a common denominator.

STEP TWO: Add or subtract the numerators.

STEP THREE: Simplify the result if needed. Notice that eg: 3/27 can be simplified, since the numerator and denominator are both divisible by 3.

And that's all there is to it! Final Answer

Watching basketball games and liking the flavor of coconut "are" independent events because the probability of a teenager from the group watching basketball games "is not equal to" the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.

Independent events is the events which occur freely of each other. An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.

We observe that the event of watching basketball games does not affect liking the flavour of coconut, hence they are independent events their probabilities are most likely not the same.

Therefore, we use "are" for the first statement to show the two events are independent and "is not equal to" for the probability statement.

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If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

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The circumcenter theorem states that the circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle. In other words, the circumcenter is the center of a circle that passes through all three vertices of the triangle.

The circumcenter theorem is a fundamental theorem in geometry and is used in the construction of the circumcenter of a triangle. The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle, and its coordinates can be determined by the coordinates of the triangle's vertices.

This theorem is useful in many applications, such as in: the construction of a triangle from its circumcenter, or in determining the distance between two points. It can also be used to determine the area of a triangle from its three vertices. The circumcenter theorem has been studied for centuries, and it is still an important tool for geometers and mathematicians today.

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Answer:

y=x^2 + 1

Step-by-step explanation: the second parabola is only raised by 1 unit up, therefore the entire function shifts upwards by 1.

The equation of the tangent line to the curve at the given point (−3, 3, 1) (asteroid) is y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Applying implicit differentiation, the equation of the tangent line is given by:

y - [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] (x+3)

The equation of a line tangent to a function f(x) at a point (x0, y0) is given by:

y-y0 = f'(x0,y0)(x-x0)

In this problem, point (-3, [tex]\sqrt{3}[/tex]), thus x0 = -3, y0 = [tex]\sqrt{3}[/tex]

The function is:

[tex]x^{2} /3+ y^{2}/3 = 4\\[/tex]

To find the derivative, we have to apply implicit differentiation, thus:

[tex]2x/3* dx/dx + 2y/3*dy/dx = 0[/tex]

[tex]2y/3*dy/dx = -2x/3[/tex]

[tex]dy/dx = -x/y[/tex]

Thus:

[tex]f(-3, \sqrt{3)} = -(-3/\sqrt{3} * \sqrt{3}/\sqrt{3})[/tex] = [tex]\sqrt{3}[/tex]

Then, the equation to the line tangent is:

y-y0 = f'(x0,y0)(x-x0)

y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Refer to this complete question:

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x2/3 + y2/3 = 4 (−3, 3, 1) (asteroid).

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Regroup means regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Given that,

We have to find what does it mean to regroup.

We know that,

When performing operations like subtraction and addition, regrouping is accomplished by creating groups of tens. Regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Because you must rearrange the numbers into place value to complete the procedure, it is known as regrouping. Regrouping is an excellent approach to simplify complicated mathematics, especially for kids. Regrouping with subtraction is sometimes referred to as "borrowing."

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The parameter (the regression coefficient) indicates the degree to which the line slopes upwards or downwards by indicating the amount by which a change in x must be multiplied by the corresponding average change in y, or the amount by which y changes for each unit increase in x.

Understanding Linear Regression Coefficients, A positive coefficient indicates that the mean of the dependent variable tends to rise in tandem with an increase in the independent variable's value. A negative coefficient indicates that the dependent variable tends to decrease as the independent variable rises.

In a regression model, the statistical measure known as R-Squared (also known as R2 or the coefficient of determination) is used to figure out how much of the variance in the dependent variable can be explained by the independent variable. In other words, the goodness of fit, or r-squared, measurement indicates how well the data fit the regression model.

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A system of linear inequalities to describe this situation are as follows;

x + y ≤ 100

3x + 5y ≥ 360

x ≥ 20

The system of inequalities has been solved graphically and one possible solution is selling 20 tacos and 80 burritos.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of tacos sold and number of burritos sold respectively, and then translate the word problem into algebraic equation as follows:

Since Henry only has enough supplies to make 100 tacos or burritos, we have;

x + y ≤ 100

Also, Henry sells each taco for $3 and each burrito for $5 and must sell no less than (at least) $360 worth of tacos and burritos each day

3x + 5y ≥ 360

Lastly, Henry must sell no less than (at least) 20 tacos;

x ≥ 20

In conclusion, you should use a graphing calculator to plot the system of linear inequalities as shown in the image attached below.

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Answer:

$77.50

Step-by-step explanation:

Since each cookie cake feeds 6, she can buy enough cakes to feed 6, 12, 28, 24, 30, 36, etc. people.

The smallest number above 29 she can feed is 30.

Each cookie cake feeds 6.

30/6 = 5

She needs to buy 5 cookie cakes.

5 × $15.50 = $77.50

The restriction on the variables x and y are given as follows:

x ∈ W, y ∈ W.

The three sets of numbers that appear in this problem are given as follows:

The number of tickets sold cannot assume decimal values, hence we know two things:

The number of tickets also assumes only values of zero or positive numbers, they cannot be negative, hence it is a whole number and the second option is correct.

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The monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

What is monthly take home pay?

The amount of money left over after taxes, benefits, and other deductions from a paycheck is known as take-home pay. It is the difference left over after subtracting all gross income deductions.

Let,

Number of hours per week = 46 weeks.

Regular hourly wage up to 40 hours = $15.90

Wage up to 40 hours = 40 x 15.90 = $636

Hours over 40 hours, wage is 1.5 times as much

Wage of hour  41 - 46 = 6 x 1.5 x 15.90 = $143.10

Total weekly wage = 636 + 143.10 = $779.10

Since 1 month = 4.345 weeks.

Therefore,

Monthly wage = Weekly wage x 4.345

                        = 777.10 x 4.345

Monthly wage = $3385.19

Now maximum and assurance = 23% of monthly wage

= 23% of 3385.19

= 0.23 x 3385.10

= $778.59

Therefore,

Monthly take home pay = Monthly wage - Tax

                                        = $3385.19 - $778.59

Monthly take home pay = $2606.6

Hence, the monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

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The volume of the tissue box is 85⅓ cubic inches.

The correct answer option is option D

Volume of the tissue box = Base area of the rectangular prism × Height of the rectangular prism

= 16 square inches × 5⅓ inches

= 85⅓ cubic inches

Therefore, the rectangular prism has a volume of 85⅓ cubic inches

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Answer:

24 square units

Step-by-step explanation:

1/2 times base times height is the formula for the area of a triangle

the base is 12

the height is 4

1/2(12)(4)

6(4)

24

hopes this helps please mark brainliest

The perimeter of the parallelogram will be D. 2✓26 i+ 8.

It should be noted that the perimeter of the parallelogram will be calculated by using the formula for distance between point.

For WX, the coordinate are (-2, 4)(2, 4)

d = ✓2 - (-2)² + (4 - 4)²

= ✓16 - 0.

= ✓16

= 4

For XY, this will be illustrated as:

d = ✓(1 - (2)² + (-1 - (4)²

= ✓1² + 5²

= ✓1 + 25.

= ✓26

Since the other sides are parallel, the perimeter of the parallelogram will be:

= 2(4) + 2✓26

= 2✓26 + 8

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The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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The average price of the stock over the first eight years is 50.69 units / year .

Given :

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function :

S ( t ) = 37 + 16 e^0.04t.

We find the average value of the stock ,

[tex]f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx[/tex]

[tex]f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx[/tex]

[tex]f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt[/tex]

= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( [tex]e^{-0.04 * 8 }[/tex] - [tex]e^{-0.04 * 0[/tex])

= 50.69 units / year.

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Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Therefore ,the true bearing of the plane and its speed is ∝=-71.9° and 324.31 mph

A thing with both magnitude and direction is called a vector. A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector. From the vector's tail to its head is the direction of motion. According to the definition of a resultant vector, a single vector is one that has the same result as several other vectors taken together.

Here,

To find the true bearing of the plane and its speed.

We find the vector component,

Since  N75°W is same as 95°+90°=165°

Thus,

f(x)=300cos100 +50cos165 = -100.39

f(y)=300sin100 +50sin165= 308.38

next we find resultant

R=[tex]\sqrt{f(x)^{2}+f(y)^{2} }[/tex]

R=[tex]\sqrt{(-100.39)^{2}+(308.38)^{2} }[/tex]

R=[tex]\sqrt{105178.35}[/tex]

R=324.31 mph

The bearing of the plane=> ∝=[tex]tan^{-1}[/tex](308.38/-100.39)

So  ∝=-71.96°

Therefore ,the true bearing of the plane and its speed is ∝=-71.96° and 324.31 mph

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Cumulative markup percent for department at the end  is 23.1%.

The men's furnishing department had an opening inventory of $168,000 at cost  with a markup of 48.5%

Cumulative markup is  the difference between the total wholesale cost and total retail price of all merchandise handled during a given period of time.

cumulative markup dollars are the total markup dollars on all merchandise for a selected selling period. To calculate cumulative markup dollars and cumulative markup percent, the following formulas are utilized by the retailer:

Cumulative Markup $ = Total Retail $ - Total Cost $

Cumulative Markup % = Cumulative Markup $ ÷ Cumulative Retail $

Steps for calculating cumulative markup percentage for the specified period of time:

Step 1. Calculate the unknown retail value for either opening inventory or purchases.

Step 2. Calculate total retail of opening inventory and purchases.

Step 3. Calculate the unknown cost value for either opening inventory or purchases.

Step 4. Calculate total cost of opening inventory and purchases.

Step 5. Calculate total markup dollars.

Step 6. Calculate cumulative markup percent for the specified period of time.

For opening inventory

retail = $168,000

cost = 168,000*48.5/100 = $81480

For purchases

retail = 80,000*52.5/100 = $42000

cost  = $80,000

total retail of opening inventory and purchase =

168,000+42000 = $210000

total cost of opening inventory and purchase =

81480+80,000 = $161480

total markup = total retail - total cost

total markup  = 210000-161480 = 48520

cumulative markup percent = (total markup/ total retail)

= (48520/210000)*100

= 0.23104761904*100

=23.1%

So cumulative markup percent for department at the end  is 23.1%.

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The obtained stress which is acting from every direction is at 45 degree.

The transformation equations will be used to calculate the stresses acting on an inclined element.

(σ x+σ y )/2  =75 MPa

(σ x-σ y )/2  =35 MPa

Tor xy = 28 MPa

sin 2θ = sin 90° = 1          

cos 2θ = cos 90° = 0

Substituting these values into Eqs

σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ      

= 130 MPa

τ x 1 y 1 =  (σ x-σ y )/sin2θ + τxy cos2θ

σ y 1=  (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ    

= 47Mpa

Elements of stress

We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.

The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.

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The factored form of the equation x² + 3x - 10 is  (x - 2)(x + 5)  .

In the question ,

it is given that ,

the equation is x² + 3x - 10 , we have to express it in factor form ,

So , rewriting the equation by using the split the middle term method .

= x² + 3x - 10

= x² + 5x - 2x - 10     , ...because   5x - 2x = 3x

taking  x common from the first two terms ,

we get ,

= x(x + 5) - 2(x + 5) taking (x+5) common from both the terms ,

we get ,

= (x - 2)(x + 5)

Therefore , the factor form is  (x - 2)(x + 5) .

The given question is incomplete , the complete question is

What is the factored form of x² + 3x - 10  ?

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The pooled proportion is  [tex]\bar{p}[/tex]=0.64.

The value of test statistic is z=1.614.

In statistical tests, which are formal procedures for drawing inferences or taking choices based on data, two different sorts of conjectures are employed: the null hypothesis and the alternative hypothesis. Based on a sample of the population, the hypotheses are suppositions regarding a statistical model of the population. In order to distinguish between statistical noise and scientific claims, tests, which are fundamental components of statistical inference, are frequently utilized in the interpretation of scientific experimental data. The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance. For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.

Given,

The pooled proportion is:

[tex]\bar{p}[/tex]=(X₁+X₂)/(n₁+n₂)

=(70+90)/(100+150)

=160/250

=0.64

Therefore, the pooled proportion [tex]\bar{p}[/tex]=0.64.

The value of test statistic is:

Test statistic=0.1/0.062

=1.614

Therefore, the value of test statistic is z=1.614.

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Answer: I added a bit more answers the one that answers your question is underlined.

a. Reject H0 when z>1.65

b. p=0.64

c. z=1.614

d. We reject the null hypothesis

Step-by-step explanation:

b. p=[tex]\frac{70+90}{100+150} =\frac{160}{250}=0.64[/tex]

c. z=[tex]\frac{0.70-0.60}{\sqrt{0.64(1-0.64)\sqrt{\frac{1}{100}+\frac{1}{150} } } }[/tex]=1.614

The domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

        |x| = x   |   x ≥ 0

        |x| = -x  |   x < 0

We have the following function -

g(x) = |x +3|

Refer to the graph attached. It can be seen that -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

Therefore, the domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

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After reflecting the quadrilateral EFGH across the line y = 2, the x-coordinates of the corresponding points in the image and the preimage will be the same.

Generally,  Reflection is an isometry, which means that it preserves distance and angles. Therefore, the x-coordinates of the points in the image and the preimage will not be changed by the reflection. The y-coordinates will change since the reflection flips the points over the line of reflection.

For example, if quadrilateral EFGH has a vertex at (x, y), then the corresponding vertex in the image will be at (x, 2 - y). The x-coordinate remains the same, but the y-coordinate is reflected across the line y = 2.

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After solving the equation, the system which has infinitely many solutions will be equal to 2x + y = 3.  Hence, option A is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given equation in the question,

6x + 3y = 9  (i)

The system for  infinitely many solutions will be,

Divide the equation (i) by three,

(6x + 3y)/3 = 9/3

2x + y = 3

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Answer:

A) y + 2x = 3

Step-by-step explanation:

Answer: ABC and AED are congruent by SSS. SSS is if three sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent. AB and AE are both 7, BC is congruent to ED and CA is congruent to DA because of the tick marks.