the Johnsons want to cover their backyard with new grass their backyard is rectangular with a length of 3x - 2 feet and a width of 3x + 1 ft however there rectangular swimming pool along with its surrounding patio has dimensions of x + 4 by x + 5 ft what is the area of the region of the yard that they want to cover with new grass

Answer:

DF = 458

Step-by-step explanation:

In statistics, T-test have an extensive application. T-tests are used in hypothesis testing or inference about the population mean when the population standard deviation is not known. Nevertheless, they are used in making inference in paired samples or dependent samples t-test as well as independent samples.

The degrees of freedom, DF, is a characteristic of the student's t distribution which is used in T-tests. In a simple T-test;

DF = n - 1

where n is the sample size

Given n is 459, DF = 459 - 1 = 458

Therefore, DF = 458

Withdrawing money from an account is a negative value, losing yards in a game would also be a negative value.

A rise in temperature would be a positive value.

Both 1 and 2 could be written as -17.

The answer is C.

Answer:

6x²

Step-by-step explanation:

to find the GCF we look at the terms and see what they have in common

we see that the greatest number both can be divided by is 6

we also look at the variables. both contain an x², so we can factor out as well

the answer would be 6x²

ANSWER

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

EXPLANATION

The polar form of a complex number ,

[tex]z = x + yi[/tex]

is given by:

[tex]z = r( \cos( \theta) + i \sin( \theta) )[/tex]

where

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

The given complex number is:

[tex]z = 4 - 10i[/tex]

[tex]r = \sqrt{ {4}^{2} + {( - 10)}^{2} } [/tex]

[tex]r = \sqrt{16 + 100} [/tex]

[tex]r = \sqrt{116} = 2 \sqrt{29} [/tex]

And

[tex]\theta= \tan^{ - 1}(\frac{ y}{x} )[/tex]

[tex]\theta= \tan^{ - 1}(\frac{ - 10}{4} )[/tex]

[tex]\theta= 292 \degree[/tex]

Hence the polar form is :

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

Answer:

Step-by-step explanation:

We must calculate the probability that the cows have a gestation time of less than 270 days. If X represents the gestation time of a randomly selected cow, then we look for:

[tex]P (X <270)[/tex]

Acora we calculate the Z-score

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

In this case

[tex]\mu=284\ days\\\\\sigma = 12\ days[/tex]

So

[tex]P (X <270) =P (\frac{X-\mu}{\sigma} <\frac{270-284}{12})=P(Z<-1.167)[/tex]

Looking in the normal standard table we have to

[tex]P(Z<-1.167)=0.1216[/tex]

Finally, the expected number of calf "E" that will have a gestation time of less than 270 days is:

[tex]E=820*P (X <270)\\\\E=820*0.1216[/tex]

E=99.71≈100 Calfs

Answer:

50 miles

Step-by-step explanation:

Addition:

7/8 + 9/4 = 7/8 + 18/8 = 25/8 inches.

Now we have to convert to miles:

25/8 inches *16

Answer = 50 miles.

Answer:

[tex]a_0 = -6[/tex]

[tex]a_1=8[/tex]

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

Step-by-step explanation:

The equation of the circle has the following form

[tex]x^2 + y^2 + a_0x + a_1y=0[/tex]

The equation of the circle has the following form

We know that the circle goes through the following points

(0, 0)

(6, 0)

(0, -8).

Then we substitute the values of x and y in the equation

For (0, 0)

[tex]0^2 + 0^2 + a_0(0) + a_1(0)=0[/tex]

[tex]0=0[/tex]

For  (6, 0)

[tex]6^2 + 0^2 + a_0(6) + a_1(0)=0[/tex]

[tex]36 + 6a_0=0[/tex]

[tex]a_0 = -\frac{36}{6}\\\\a_0 = -6[/tex]

For (0, -8)

[tex]0^2 + (-8)^2 + a_0(0) + a_1(-8)=0[/tex]

[tex](-8)^2 - 8a_1=0[/tex]

[tex](-8)^2 = 8a_1[/tex]

[tex]a_1=8[/tex]

Finally the equation is:

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

Answer:

C

Step-by-step explanation:

4 divided is said first, so it comes first in the equation. Difference means subtraction, meaning h - 7

Answer:

Part 11) The cyclist stops for a time during the section B

Part 12) He traveling slowest in section A

Part 13) He traveling fastest in section C

Part 14) The speed in section D is 20 km/h

Part 15) The cyclist was 60 km from home when he turned around

Step-by-step explanation:

we know that

The speed is the ratio of the distance by the time

s=d/t

The slope of the graph is equal to the speed of the cyclist

Part 11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop?

The cyclist stops for a time during the section B

Because, during section B the distance is a constant (d=30 km)

therefore

The speed is equal to zero (Remember that the slope of a horizontal line is equal to zero)

Part 12. During which labeled section was he traveling the slowest?

Find the slope (speed) in each section

Find the slope in section A

Let

A(0,0) and B(4,30)

the slope is equal to

m=(30-0)/(4-0)=7.5 km/h

Find the slope in section B

Is a horizontal line

therefore

the slope is equal to

m=0 km/h

Find the slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h

Find the slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

He traveling slowest in section A

Part 13. During which labeled section was he traveling the fastest?

Remember part 12)

Slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h ----> is the greater slope

therefore

He traveling fastest in section C

Part 14. Calculate the speed of the cyclist during section D

Remember part 12)

Slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

The speed in section D is 20 km/h

Part 15. How far away was the cyclist when he turned around and headed home

Observing the graph

we know that the cyclist turned around at point (7,60)

therefore

The cyclist was 60 km from home when he turned around

Answer:

That is an octagon (eight sides).

Interior Angle Total = 1,080

EACH interior angle = 180 - (360 / 8) = 135

n + 161 + (n -12) +(n + 30) + n + 134 + (n+16) + 126 = 1,080

5n + 455 = 1,080

5n = 625

n = 78.125

Step-by-step explanation:

So C= dxpi or rx2xpi= c in this case 7x 2 = 14 is diameter do E D and A finds the diameter and the rest do not

Answer:

(2, 2)

Step-by-step explanation:

To determine which ordered pair is a solution to the equation.

Substitute the x- coordinate into the left side and the y- coordinate into the right side and if both sides are equal then that is the solution.

(2, 2)

3 × 2 = 6 and 8 - 2 = 6 → hence (2, 2) is a solution

(8, 0)

3 × 8 = 24 and 8 - 0 = 8 → hence (8, 0) is not a solution

(3, 1)

3 × 3 = 9 and 8 - 1 = 7 → hence (3, 1) is not a solution

2\xy³z⁴ is the simplification.

Answer is D and E

Since 9 divided by 3 is three it would be correct and 4 multiplied by 9 is E would be correct. The others just don’t add up.

The equation where c = 9 should be option D and option E.

C = 9

If [tex]C \div 3 = 3\\\\[/tex]

So this should be correct as 3 = 3

And,

36 = 4c

c = 9

Learn more about the equation here: https://brainly.com/question/18715058

1,2 cause of the o and y axis

The vertex is where the parabola changes directions, or in simpler terms, at the parabolas lowest point. Unless the parabola is upside down, then the vertex is where the highest point is.

The acid of symmetry is the line where the parabola can be divided evenly. This is almost always where the vertex is, except it continues on.

The y-intercept is where the parabola intersects with the y-axis.

I’ve answered the question below in the picture (my graph is not to scale but the answers are correct for yours)

Hope this helped and good luck!!

The range of the piecewise defined function is:

                  y= -6 , y= -4 , y= -3 , y=0

The piecewise function is defined by:

f(x)  =    2x+2   when  x < -3

              x       when  x = -3

  and  -x-2      when  x > -3

Then the graph of the function is a strictly increasing function and is a line with a slope of 2.

The function increases continuously from -∞ to -4

i.e. it takes all the value in the interval (-∞,-4)

There is a open circle at (-3,-4)

The graph of the function f(x) is strictly decreasing .

Since the graph is a line with slope -1.

Also, there is a open circle at (-3,1)

and the function starts decreasing continuously and will take all the values strictly less than 1.

i.e. the range for x > -3 is:  (-∞,1)

The range of the whole function f(x) is:

                            (-∞,1)

Answer:

• 9(sin 42°)

_______

sin 29°

Step-by-step explanation:

The value of x is calculated by the sine rule is 9(sin 42°)/sin 29°. Then the correct option is B.

Trigonometry deals with the relationship between the sides and angles of a triangle.

We know that the sine rule is given as

[tex]\rm \dfrac{a}{sin A} =\dfrac{b}{sin B}=\dfrac{c}{sin C}[/tex]

Then put the values and we have

[tex]\begin{aligned} \rm \dfrac{x}{sin 42^o} &= \rm \dfrac{9}{sin 29^o}\\\\\\\rm x &= \rm \dfrac{9*sin 42^o}{sin 29^o} \end{aligned}[/tex]

More about the trigonometry link is given below.

https://brainly.com/question/22698523

The answer is:

The second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

To answer the question, we need to find which piecewise function contains the graphs shown in the picture, we have that first line shown, is decreasing and exists from the negative numbers to 0,  and the line cuts the x-axis and the y-axis at "-2", for the second line shown,  we have that is decreasing but exists from 0 (including it) to the the positive numbers.

So, finding which piecewise satisfies the function shown, we have:

- First piecewise function:

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {\frac{x}{2} }\geq 0} \right.[/tex]

First line,

We have the first line,

[tex]-x-2<0\\[/tex]

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exists from all the numbers less than 0, to 0, and it cuts the x-axis at -2 and the y-axis at -2.

Second line,

[tex]\frac{x}{2}\geq 0[/tex]

The variable has positive coefficient, meaning that the function (line) is increasing.

Hence, since the second line is not decreasing, the piecewise function is not the piecewise function shown in the picture.

- Second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

First line,

We have the first line,

[tex]-x-2<0\\[/tex]

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exist from all the numbers less than 0, to 0.

Second line,

[tex]-\frac{x}{2}\geq 0[/tex]

The variable has a negative coefficient ([tex](-\frac{1}{2})[/tex], meaning the the unction (line) is decreasing, also we can see that the function does exists from 0 (including it) to the positive numbers.

Hence, we have that the correct option is the second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

Note: I have attached a picture for better understanding.

Have a nice day!

Answer:

[tex](-5,0)[/tex] and [tex](3,0)[/tex]

Step-by-step explanation:

Think about it.

What two numbers multiply to -15 and add up to 2?

The answers are 5 and -3.

So plug that into the factored form of a parabola.

[tex]y=(x+5)(x-3)[/tex]

To find the x-intercepts, plug in 0 for [tex]y[/tex].

[tex](x+5)(x-3)=0[/tex]

Since we are multiplying, at least one of the terms has to equal 0.

[tex]x+5=0 \\ x-3=0 \\ \\ x=-5,3[/tex]

So the x-intercepts are [tex](-5,0)[/tex] and [tex](3,0)[/tex].

Answer: 3 7/10

Let's rewrite our equation with the parts separated

= 1 + 2/5 + 2 + 3/10

Now, let's add the whole numbers

1 + 2 = 3

Now, let's figure out how to solve the fraction parts

2/5 + 3/10 = ?

You'll need to find the LCD (Lowest Common Denominator) of 2/5 and 3/10.

If you don't know, the LCD is 10

Since 3/10 already has a denominator of 10, we don't need to do anything with it.

However, we need to multiply the numerator and denominator of 2/5 by 2

Why? We need the LCD, which is 10. Also, we can only add fractions if they have the same denominators

Numerator: 2 x 2 = 4

Denominator: 5 x 2 = 10

Fraction: 4/10

Now add the fractions

4/10 + 3/10 = 7/10

Finally, combine the whole numbers with the fractions

3 + 7/10 = 3 7/10

Answer:

one solution

Step-by-step explanation:

9x+16=4x

16=4x-9x

16/-5=x

x=-3.2

The median measurement of the capsules is 2317 mg, which is the average of the fourth and fifth values when listed in order. The mean measurement is also 2317 mg, found by summing all measurements and dividing by the total number of samples.

To find the median measurement of the pharmacist's recorded capsule weights, we first list the measurements in numerical order: 2310 mg, 2312 mg, 2313 mg, 2315 mg, 2319 mg, 2320 mg, 2321 mg, 2325 mg. Since there are eight measurements (an even number), the median is the average of the fourth and fifth measurements: (2315 mg + 2319 mg) / 2 = 4634 mg / 2 = 2317 mg. Therefore, the median measurement is 2317 mg.

To calculate the mean measurement, we sum all the measurements and then divide by the number of measurements: (2312 mg + 2313 mg + 2315 mg + 2321 mg + 2325 mg + 2310 mg + 2320 mg + 2319 mg) / 8 = 18535 mg / 8 = 2316.875 mg. The mean measurement, rounded to the nearest milligram, is 2317 mg.

Answer:

The distance between two points is √58 or 7.61.

Step-by-step explanation:

In the question we need to find the distance between two points 4,1 and -3,-2 given.

Distance between two points can be found using the formula:

[tex]d(P1,P2) = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]

Putting the given points in the formula we get,

x₂ = -3, x₁ = 4, y₂= -2, y₁= 1

[tex]=\sqrt{(-3-(4))^2 + (-2-(1))^2} \\=\sqrt{(-3-4)^2 + (-2-1)^2}\\=\sqrt{(-7)^2 + (-3)^2}\\=\sqrt{49 + 9}\\=\sqrt{58}\\=7.61[/tex]

So, the distance between two points is √58 or 7.61.

Answer:

4 3/4 or 19/4

Step-by-step explanation:

To answer this question, you must add the values of all of the x's on the line plot. There is 1 x on 1/4 and 2 x's on 3/8. So, add 1/4 + 3/8 + 3/8 to get 1. Next, there are 3 x's on 1/2. So, add 1 + 1/2 + 1/2 + 1/2 to get 2 1/2. Lastly, there's 1 x on 5/8, 1 x on 3/4, and 1 x on 7/8. So add 2 1/2 + 5/8 + 3/4 + 7/8 to get  4 3/4 of 19/4 as your final answer. I hope this helps!!!

Answer:

the variable is "b"

Step-by-step explanation:

Answer:

5 + 5 + 5 + 5 + 5 + 5 = 30

6 + 6 + 6 + 6 + 6 = 30

5 = 30 ÷ 6

6 = 30 ÷ 5

Answer: nina is getting $15 for 1 lawn.

Step-by-step explanation:

1      $15

2     $30

3     $45

4     $60

Answer:

Same:

A 50% decrease followed by a 100% increase.

A 33 1/3% decrease followed by a 50% increase.

Less:

A $25 increase followed by a $30 decrease.

A 20% increase followed by a 25% decrease.

Greater:

An 80% increase followed by a 40% decrease.

IN ORDER TO FIGURE OUT THE ANSWER CHOOSE A NUMBER AND APPLY WHAT IT IS TELLING YOU. FOR EX: on #1: I chose the number 100 then multiplied it by 1.8 then multiplied that number by 0.6 to get 108 which is greater than 100

80% increase followed by 40% decrease=greater

50% decrease follow by 100% increase=greater

20% increase followed by a 25% decrease=less

$25 increase followed by $30 decrease= less

33 1/3% decrease followed by 50% increase= same

Answer:

27

Step-by-step explanation:

because 6×4 is 24 and 24+3 =27

Answer:

The answer is 27

Step-by-step explanation:

Using Pemdas (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) 6 x 4= 24 then 24 + 3= 27.

Hope this helps. Please name me Brainliest