61. The true proportion p of people who give a favorable
rating to Congress is 8% with a margin of error of
1.5%. Describe this statement using an absolute
value equation.

Reflecting over y=x maps (x,y) onto (y,x).

So, the answer is A. (-8, 3).

Answer:

Step-by-step explanation:

Answer:

x = 15° , y = 125°

I hope this helps u

The area of a rectangle = Length × Breadth

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Answer:

Everything in the box currently is correct but the bottom two numbers are just -3 and -4

Step-by-step explanation:

Answer:

2x^2 + 5x - 3

Step-by-step explanation:

Area = length (a) * width (b)

(x + 3) * (2x - 1)

2x^2 + 6x - x - 3 (combine like terms)

2x^2 + 5x - 3

Brainliest, please :)

Answer:

Step-by-step explanation:

Total Students = 20 + 18 = 38 students

For boys percentage = 20/38 * 100

Boys percentage = 52.6%

For girls percentage = 18/38 * 100

Girls percentage = 47.3%

Answer:

(i) 52.631578947368 %

(ii) 47.368421052632 %

Step-by-step explanation:

there are :

20 boys  

18 girls

Total number of students 38

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

(i) the percentage of boys in the class

[tex]=\frac{20}{38} \times100 = 52.631578947368 \ \%[/tex]

(ii) the percentage of girls in the class

[tex]=\frac{18}{38} \times100 = 47.368421052632 \ \%[/tex]

Answer:

Volume = 96m^3

Step-by-step explanation:

If the length of the tank is 8 meters, then the width must be 4 meters, because the question said the width was half the length. Since the height, 3 meters, was also given, we can find the volume.

Vol = L × w × h

We multiply together the length, width and height.

Vol = 8 × 4 × 3

= 96

The volume is 96 meters^3

The complete table is

x -12 -6 3 15

y -6 5 15 15

The domain is given as:

Domain = {-12, -6, 3, 15}.

The incomplete table is given as

x

y -6 5 15 15

Enter the domain in the x values

x -12 -6 3 15

y -6 5 15 15

Hence, the complete table is

x -12 -6 3 15

y -6 5 15 15

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Answer:

y=49x

Step-by-step explanation:

As you can see from the graph, the distance from home increases by 49 miles per hour driven.

Therefore the distance driven for any given time in hours is 49x

Therefore y = 49x

The spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams and will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

The density of an object is given as the ratio of its mass and its volume.

Density = Mass/Volume.

In the question, we are informed that a spherical ball for a machine was made with a radius of 2 centimeters.

Thus, the volume of the spherical ball, using the formula for the volume of a sphere, V = (4/3)πr³, where r is its radius, can be calculated as:

V = (4/3)π(2)³ cm³ = 32π/3 cm³ = 33.51032 cm³.

The mass of the ball is given to be 278.1 grams.

Thus, its density = 278.1/33.51032 grams per cm³ = 8.2989355 grams per cm³.

We know that the density of Terbium is 8.23 grams per cm³.

Thus, the spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams, will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

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Answer: copper

Step-by-step explanation:

The approximate solution of the system of equations is x = 0.75

The functions are given as:

f(x) = x^4 + 9x^2 - 3

g(x) = (1/2)^x - 2

Calculate the values of the function from -1 to 1

x             f(x)      g(x)

-1            7          8

-0.75    2.38   6.72

-0.5   -0.69     5.66

-0.25  -2.43   4.76

0          -3       4

0.25    2.43   3.36

0.5      -0.69   2.83

0.75    2.38   2.38

1          7        2

From the above table, we have:

f(0.75) = g(0.75) = 2.38

Hence, the approximate solution of the system of equations is x = 0.75

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The equation which could be used to find the value of x is; (x+10) +(x-6) = 10.

According to the task content, it follows that the lines WX and WY both amount to the line XY which joins points X and Y.

Hence, it follows that the equation which can be used to find the value of x is; (x+10) +(x-6) = 10.

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Answer:

1. Function

2. Not a function

3. Function

4. Not a function

Step-by-step explanation:

A function just means that for each input it outputs only 1 output. This output isn't necessarily unique. So for example if you're just given: f(2) = 3 and f(1) = 3, this is a function since each input only outputs 1 value, even though the output isn't unique, but if you're given: f(3) = 2, f(2) = 1, f(3) = 3. that's not a function since f(3) outputs both 2 and 3.

Anyways now that you hopefully understand this, let's look at each image.

Relation 1: (Function)

   So for each input (the domain) it's only pointing to one output (range), even if multiple input (the domain) are pointing to the same output (the range), it's still a function.

Relation 2: (Not a function)

   This is not a function, since if you look at the input 7 (the range), you'll see it outputs two things (range). It outputs -6 and -7. So this is not a function

Relation 3: (Function)

   This is a function since each x-value (input) has only one y-value (output). So it's a function

Relation 4: (Not a functio)

   This is not a function, since there are multiply coordinates with the same x-coordinate (input) and different y-coordinates (output). The x-coordinate 2 has the output b, y, and m, and since no value is given for these variables, it can be assumed they're different values, thus it's not a function.

Answer:

D. 16, 9, 8

Step-by-step explanation:

sum of any two sides of triangles must be greater than the third side

only the fourth option follows this rule

Answer:

You didn't include any choices.....see below

Step-by-step explanation:

Place name of eights are ten thousands place & tens place & 80000, 80 are the values respectively.

The expanded form of a number is splitting of numbers based on place value. The place are ones, tens, hundreds, thousands, ten thousand etc

that is, the number represented by the sum of each digit multiplied by its place value is called the expanded form of a number.

Example : Expanded form of 4567 is 4000+500+60+7. where 4 is in thousands place, 5 is in hundreds place, 6 is in tens place and 7 is in ones place.

Given that, The speed of light is 186,282 miles per second.

The number is 186282.

Expanding the number, we get,

186282 = 100000+80000+6000+200+80+2

Here in the number 186282, eight present in the ten thousands place and in the tens place.

Since one eight is in ten thousands place, so the value is 80000

And the another eight is in the tens place, so the value is 80.

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Answer:

The evaluated function for the indicated values is given below.

The value of f(-3) is 20 .

The value of f(2) is 10 .

The value of f(-a) is [tex]$2|-3 a-1|$[/tex].

The value of -f(a) is [tex]$-2|3 a-1|$[/tex].

The value of f(a+h) is [tex]$2|3 a+3 h-1|$[/tex].

Step-by-step explanation:

A function [tex]$f(x)=2|3 x-1|$[/tex] is given.

It is required to evaluate the function at [tex]$f(-3) ; f(2) ; f(-a) ;-f(a) ; f(a+h)$[/tex].

To evaluate the function, substitute the indicated values in the given function to determine the output values and simplify the expression.

Step 1 of 5

The given function is [tex]$f(x)=2|3 x-1|$[/tex].

To evaluate the function at f(-3), substitute -3 in the given function [tex]f(x)=2|3 x-1|$\\ $f(-3)=2|3(-3)-1|$\\ $f(-3)=2|-9-1|$\\ $f(-3)=2|-10|$\\ $f(-3)=2(10)$\\ $f(-3)=20$[/tex]

Step 2 of 5

To evaluate the function at $f(2)$, substitute 2 in the given function.

[tex]f(x)=2|3 x-1|$\\ $f(2)=2|3(2)-1|$\\ $f(2)=2|6-1|$\\ $f(2)=2(5)$\\ $f(2)=10$[/tex]

Step 3 of 5

To evaluate the function at f(-a), substitute -a in the given function.

[tex]$$\begin{aligned}&f(x)=2|3 x-1| \\&f(-a)=2|3(-a)-1| \\&f(-a)=2|-3 a-1|\end{aligned}$$[/tex]

Step 4 of 5

To evaluate the function at -f(a), substitute a in the given function.

[tex]f(x)=2|3 x-1|$\\ $-f(a)=-2|3(a)-1|$\\ $-f(a)=-2|3 a-1|$[/tex]

Step 5 of 5

To evaluate the function at f(a+h), substitute a+h in the given function. [tex]$f(x)=2|3 x-1|$[/tex]

[tex]$$\begin{aligned}&f(a+h)=2|3(a+h)-1| \\&f(a+h)=2|3 a+3 h-1|\end{aligned}$$[/tex]

The algebraic expression of the given sentence is: 7(x - 1).

Let the unknown number be represented as x.

The word "difference" means subtraction which is "-". Multiplied means times.

We would have the following:

"Difference of x and 1" is: x - 1

x - 1 multiplied by 7 would be: 7(x - 1)

Therefore, the algebraic expression is: 7(x - 1).

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The product of the polynomials, (x + 2)(x - 2) = x² - 4.

Given the following expression, (x + 2)(x - 2), to find the product, apply the distributive property as shown below:

(x + 2)(x - 2)

x(x - 2) + 2(x - 2)

x² - 2x + 2x - 4

Combine like terms together

x² - 4

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The order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

From the question, we are to order the given numbers from the greatest to the least in magnitude

The given numbers are

|-20|, |-4|, |-6|, |8|, |2 3/10|, |12.3|

Since the modulo sign is included, the negative signs do not take effect.

Hence, the order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

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Answer:

The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2

Step-by-step explanation:

Two points are given in question, (2,4) and (4,10).

It is required to find out a linear equation satisfying the points (2,4) and (4,10).

To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]

Step 1 of 3

The slope of a line passing through the points (2,4) and (4,10) is given by

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$$[/tex]

Step 2 of 3

Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-4)=3(x-2)$$[/tex]

Distribute 3 ,

[tex]$$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$$[/tex]

Step 3 of 3

This linear function can be written in the slope-intercept form by adding 4 on both sides,

[tex]$$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$$[/tex]

So, this is the required linear equation.

Based on the lateral area of the cylinder, the volume of the cylinder can be calculated to be 139.5 cm³.

When given the lateral surface area of a cylinder, you can find the volume as:

= Area of lateral surface x (radius / 2)

Solving gives:

= 55.8 x (5 / 2)

= 55.8 x 2.5

= 139.5 cm³.

Missing part of the question:

Radius of the cylinder is 5cm.

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Using proportions, it is found that Mason ran 620 meters.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the ratio, the rule of three is given as follows:

2 laps for Mason - 3 laps for Laney.

n meters for Mason - 930 meters for Mason.

Applying cross multiplication:

3n = 930 x 2

n = 930 x 2/3

n = 620

Mason ran 620 meters.

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Answer:

B or the second option

Step-by-step explanation:

We can label the diagram parts A-E to fully represent the situation in the question.

A: Julie's ascent up the mountain (moving/increasing)

B: Julie drinking hot chocolate (stationary/constant)

C: Julie's descent down the mountain (moving/decreasing)

D:  Julie rests (stationary/constant)

E:  Julie's final descent down the mountain (moving/decreasing)

The function of the linear equation shows that the slope(m) = -7, the x-intercepts is (-1/7,0), and the y-intercepts is (0,-1)

The function of a linear equation takes the form y = ax + b. In this situation, the values of y can be determined when x = 0, and the values of x can be determined when y = 0

From the given information:

y = f(x) = -7x - 1

We can determine the:

y = -7x - 1

Slope (m) = -7

Set the values of y = 0 to determine the x-intercepts.

0 = -7x - 1

7x = - 1

x = -1/7

x-intercepts = (-1/7, 0)

Set the values of x = 0 to find the y-intercepts.

y = -7(0) - 1

y = - 1

y-intercepts = (-1, 0)

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Answer:

Step-by-step explanation:

There are 26 letters, so there are 26

3

 possible 3-letter sequences.

the number of these which are palindromes can be computed as follows:

26 choices for the first letter

26 choices for the second letter

1 choice for the third letter ( it has to agree with the first)

number of ways  =26

2

Probability of a letter palindrome =26

2

/26

3

=1/26

there are 10 digits, so there are 10

3

 sequences of digits.

Reasoning as above, the number of digit-palindromes is (10)(10)(1)=10

2

so the probability of a digit-palindrome is 10

2

/10

3

=1/10

The events

D - digit palindrome

L - letter palindrome

are independent but not mutually exclusive.

So, P(LorD)=P(L)+P(D)−P(LandD)

P(LorD)=P(L)+P(D)−P(L)P(D)

=1/26+1/10−(1/26)(1/10)

=10/260+26/260−1/260

=35/360=7/52

Answer:

B

Step-by-step explanation:

Answer:

I think it is 72

Step-by-step explanation:

but the question doesn't make sense because it should tell the number of spoons per 1 cup of sugar, perhaps it was a copy-paste mistake?

The coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

The linear equation is given as:

-3x + 4y= 19

Set x = 0

So, we have:

-3(0) + 4y = 19

Evaluate

4y = 19

Divide by 4

y = 19/4

Hence, the coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

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