y-7 = (12-x)2 in vertex form

The solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

Given that;

4(sin x)² - 2 = 0

Add 2 to both sides and divide both sides 4

4(sin x)² - 2 + 2  = 0 + 2

4(sin x)²  = 2

(4(sin x)²)/4  = 2/4

(sin x)²  = 1/2

Square both sides

√((sin x)²)  = ±√(1/2)

sin x = ±√(1/2)

sin x = ±(√2)/2

Next, we solve for x

Not that 180° = π

x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4

x = π/4

Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.

x = π - π/4

x = 3π/4

Now, we find the period of sin x

2π / |b|

We know that, the distance between a number and zero is 1

2π / 1

2π

Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.

Since sine function is negative in third and fourth quadrant,

x = 2π + π/4 + π

x = 5π/4

Now, add 2π to every negative angle to get a positive angle

x = 2π + ( - π/4 )

x = 2π×4/4 - π/4

x = ((2π × 8) - π ))/4

x = (8π - π)/4

x = 7π/4

Therefore, the solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

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Based on the amount that Nader can pay per month, and the interest rate as well as the period, the amount he could spend if the rate was annual is $8,385.33.

If Nader can pay $280 per month, the amount he can pay per year i:

= 280 x 12

= $3,360

The amount that he can spend on the car is the present value of these yearly payments:

= 3,360 x (1 - (1 + 9.8%)⁻³) / 9.8%

= 3,360 x 2.49563439768461

= $8,385.33

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The true statement ae:
Both have the same number of data points.

Both means are between 3 and 4.

Westwood has less variability than Middleton.

A dot plot is made up of dots which represents the frequency of the values in the data set and a numberline.

The total number of data points for both dot plots is 20.

The range of Middleton is : 9 -1 = 8

The range of Westwood is: 6 - 2 = 4

Middleton has more variability than Westwood.

Mean sum of numbers / total numbers

Middleton = (1+ 2+  2 + 2 + 2 +  3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 +  5 + 5 + 5, 5 + 6 + 9) / 20 = 3.75

Westwood = ( 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 6) / 20 = 3.85

Here is the complete question:

The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?

Check all that apply.

Both have the same number of data points.

Both means are between 3 and 4.

Both have the same median.

Both have the same range.

Westwood has less variability than Middleton.

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Answer:  Either [tex]w(w-4)[/tex] or [tex]w^2 - 4w[/tex]

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

Explanation:

w = width

w-4 = length since it is 4 less than the width

Multiply the length and width to get the area of the rectangle.

area = length*width

area = [tex](w-4)w[/tex]

area = [tex]w(w-4)[/tex]

area = [tex]w^2-4w[/tex]

In the last step, I used the distributive property.

Either expression mentioned above is valid for the area. If you had to pick only one, I'd go for [tex]w^2-4w[/tex]

Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional

In the given diagram,

If

[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]

Then,

Line AE is parallel to line BD

From the given information,

|AB| = x = 9

|ED| = 5

|AC| = 9 + 11 = 20

|EC| =5 + 7 = 12

Thus,

[tex]\frac{9}{20}=\frac{5}{12}[/tex]

20 × 5 = 9 × 12

100 ≠ 108

∴ The lines are not parallel

Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional

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The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]

Using the formula, we have that [tex]P_{100} = 2530[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

From the recursive formula, we have that:

[tex]a_1 = 30 + 25 = 55, d = 25[/tex]

Hence the explicit formula is:

[tex]P_n = 55 + 25(n-1)[/tex]

[tex]P_n = 30 + 25n[/tex]

Then, when n = 100:

[tex]P_{100} = 30 + 25(100) = 2530[/tex]

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The computation shows that the number of possible ways will be 12.

From the information given, Mary has four t-shirts-T₁, T2, T3, and T4, and three pairs of jeans-J1, J2, and J3.

Therefore, the number of possible ways that she can choose her outfit will be:

= 4 × 3 = 12

In conclusion, the correct option is 12.

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Answer:

t=5.5

Step-by-step explanation:

The ball hits the ground when h = 0.

[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]

However, as the answer must be positive, t=5.5

Answer:

The parallel slope for this equation is going to be [tex]\frac{3}{4}[/tex] hope that helps and can you mark me as brainlist please.

Answer:

x = -4, 1

Step-by-step explanation:

Since we have a absolute value function here, we can tell there is goning to be multiple values.

First we will find x with the original function since we know |5| = 5.

Given f(x) = 5 = -2x-3,

[tex]2x-3 = 5 \\

-2x-3+3 = 5 + 3 \\

-2x = 8 \\

x = \frac{8}{ - 2} \\ = - 4[/tex]

Now we also know that |-5| = 5 as well (absolute value)

Given |-2x-3| = |-5|,

[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]

You can verifiy these 2 values by substituting them into the equation.

f(-4) = |-2(-4)-3|

= |8-3|

= |5|

= 5

f(1) = |-2(1)-3|

= |-2-3|

= |-5|

= 5

A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.

A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.

The function is given as,

f(x) = |-2x-3|

which implies that f(x) = -2x - 3 for x > 0 and  f(x) = -(-2x - 3 )for x < 0

As per the question ,

Substitute the value of f(x) = 5, for both the cases to get the value of x as,

-2x - 3 = 5  and -(-2x - 3 ) = 5

=> x = -4 and x = 1.

Hence, the values of x obtained for the given condition are x =-4 and x = 1.

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Answer:

Angle rotation 120 ,90,60,45

B. The standard deviation is he square root of variance. The larger the standard deviation the more variation

Answer:

this is quite an easy problem.

Step-by-step explanation:

The problem appears to be asking for the class with the greatest variability of test 1, which merely means that you are looking for the graph that has the most distributed test scores. The graph that shows the largest difference in each test score will be your answer.

Fundamental Theorem of Arithmetic is not a method for solving a system of equations.

A system of equations is a collection of two or more equations with a same set of unknowns.

The system of equation can be solved using the following method.

The graphing involves using graph to find the intersection of the system of equation.

Substitution method involves substituting one variable to another.

Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations

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Answer:

first equation

Step-by-step explanation:

Answer: [tex]6.67m^3[/tex]

Step-by-step explanation:

For hemisphere...

diameter (d1) = 3m

radius (r1) = (3/2)m

The total volume of the hemisphere

[tex]v1=\frac{2}{3} \pi (r1)^3[/tex]

[tex]=\frac{2}{3} \pi (\frac{3}{2} )^3[/tex]

[tex]=\frac{9}{4} \pi[/tex]

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

For smaller cylinder

diameter (d2) = 0.75

radius (r2) = 0.75/2m

height (h2) = 0.80m

Volume of smaller cylinder

(V2) = [tex]\frac{1}{3} \pi (r2)^2h2[/tex]

[tex]=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80[/tex]

[tex]=\frac{3}{80} \pi[/tex]

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

For bigger cylinder

Volume of bigger cylinder =

[tex]V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70[/tex]

[tex]=\frac{35}{384} \pi[/tex]

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

Volume of water =  [tex](v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3[/tex]

Answer:

w x 6

Because W is a variable and we don't know what W so it the equation is gonna be a open sentance

Using the Poisson distribution, it is found that:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The average rate is of 3 no-hitters per season, hence:

[tex]\mu = 3[/tex].

The probability that an entire season elapses with a single no-hitter is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]

There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.

Seasons are independent, hence:

If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.

The probability that there are more than 3 no-hitters in a single season is P(X > 3) given as follows:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}3^{3}}{(3)!} = 0.2240[/tex]

Then:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.6472 = 0.3528[/tex]

There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.

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The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.

Exponential functions are are written as y(x) = abˣ

Here

a is the initial population

b is the rate of growth or decrease

x is the time taken

The Given exponential function is

[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]

From the standard equation of Exponential function

(a) a = 1200 and 1000 is the initial population of the bacteria

(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies

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The profit for the Golfing Emporium is $160.

We know that profit is defined as the difference between the revenue and the cost.

Here, we know that on the sale, the Golfing Emporium sells the set of clubs at $780 (this is the already discounted price).

While when they buy the set, the pay $620 for it.

Then the profit is given by:

P = $780 - $620 = $160

The profit for the Golfing Emporium is $160.

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Answer:

17

Step-by-step explanation:

f(5) means replacing any x in the equation with 5, so that would give you 3*5 + 2

in order of operations, 3*5 = 15 + 2 = 17

hope this helped! :)

Answer: (-6:5)

Step-by-step explanation:

6/5 = 1.2

-1 * 6 = -6

-6/5 = -1.2

thus...

Ratio = (-6:5)

Answer:

D

Step-by-step explanation:

well, you can simply put the arguments where belong and if you check choice D

5(1)–2(2)=1

so that will be the answer

The estimated total of 674, 692, 724, and 739 is: 2800.

To find the sum using clustering estimation technique first step is to round each number to the nearest 10s.

674 into 670

692 into 690

724 into 720

739 into 740

Second step is to add

Addition=670+690+720+740

Addition=2820

2820 to the nearest 100s is 2800.

Therefore the estimated total of 674, 692, 724, and 739 is: 2800.

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Using the normal distribution, we have that:

The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of men's heights are given as follows:

[tex]\mu = 69.3, \sigma = 3.9[/tex].

The proportion of men who meet the height requirement is is the p-value of Z when X = 62 subtracted by the p-value of Z when X = 55, hence:

X = 62:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{62 - 69.3}{3.9}[/tex]

Z = -1.87

Z = -1.87 has a p-value of 0.0307.

X = 55:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 69.3}{3.9}[/tex]

Z = -3.67

Z = -3.67 has a p-value of 0.0001.

0.0307 - 0.0001 = 0.0306 = 3.06%.

The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.

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The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.

A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '

A statement is called a contradiction if the final column in its truth table contains only 0's.

A tautology is a statement that is always true.

The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

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Based on the Venn diagram, the elements in set A can be found to be 2, 3 ,5, 7,and 9.

The elements in set A would be those which are in A alone and in set B as well.

The numbers in set A alone are:

7, 3, 5, 9

The number in set B and A is 2.

The elements in set A is therefore:

2, 3 , 5, 7,and 9

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Answer:

[tex]\sf C. \quad \dfrac{1}{9}[/tex]

Step-by-step explanation:

Addition Law for Probability

[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]

Given:

  [tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]

  [tex]\sf P(B)=\dfrac{2}{9}[/tex]

  [tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]

Substitute the given values into the formula and solve for P(A ∩ B):

[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]

[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]

We want to find a prime number greater than 10 and less than 19.

* What is a prime number?

Prime number is a number that cannot be divided by any number other than 1 and itself

There are so many possibilities:

Ellie's street address could be 11, 13 or 17

Hope it helps!

Using the mid-point concept, the best restaurant for them to meet is given by:

Greek restaurant at (–25, –15).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For the midpoint between his house and his mom's, the coordinates are given as follows:

Hence the Greek restaurant is the best option, as it is closest.

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Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.

Substituting into point-slope form,

[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]