Anita and Joelle bowled together and their combined total score for one game was 425 points. Anita’s score was 40 less than twice Joelle’s. What were their scores? Write a system of equations to model the problem if x represents Joelle’s score and y represents Anita’s score.

First, we establish our hypothesis:

Null hypothesis H0: μ = $1.00  

Alternative hypothesis Ha: μ ≠ $1.00

Let’s say X  = the sample average cost of a daily newspaper = 0.96

u = population mean cost = 1.00

S = sample standard deviation = 0.18

Calculating for z value:

z = (X – u) / S

z = (0.96 – 1) / 0.18

z = – 0.222

From the standard distribution table at this z value, p-value = 0.4129

Since alpha = 0.01, the decision therefore is:

Do not reject the null hypothesis because the p-value is greater than 0.01. There is enough evidence to support the claim that the mean cost of newspapers is $1. 

The division to the expression Divide 40x/ 64y by 5x/ 8y is (a) 1

From the question, we have the following parameters that can be used in our computation:

Divide 40x/ 64y by 5x/ 8y

As an expression we have

40x/ 64y ÷ 5x/ 8y

So, we have

40x/ 64y ÷ 5x/ 8y = 40x/ 64y * 8y/5x

Divide the variables

This gives

40x/ 64y ÷ 5x/ 8y = 40/64 * 8/5

Lastly, we have

40x/ 64y ÷ 5x/ 8y = 1

Hence, the solution to the expression is (a) 1

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8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.

To multiply 8 times the square root of 3 by 9 times the square root of 27, we can simplify the expression using the properties of square roots and perform the multiplication.

First, let's simplify the square roots:

Square root of 3 can be written as √3.

Square root of 27 can be written as √(9 * 3), which further simplifies to √9 * √3 = 3 * √3.

Now, we have:

8 * √3 * 9 * √27 = 8 * √3 * 9 * (3 * √3) = 8 * 9 * 3 * √3 * √3 = 216 * 3 * √3 * √3.

Since the square root of 3 multiplied by itself (√3 * √3) simplifies to 3, we have:

216 * 3 * 3 = 1944.

Therefore, 8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.

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Answer: The number 3 is missing from the table!

Step-by-step explanation:

The required ratio of area of cubes is 25 : 16.

Volume of cube 1 = 125
Volume of cube 2 = 64

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Volume of cube 1 = 125
    a³ = 125
    a = 5
Volume of cube 2 = 64
       A³ = 64
        A = 4
Area of cube 1 = a² x 6
= 5² x 6
= 150
Area of cube 2 = A² x 6
= 4² x 6
= 96
Now ,
The ratio of areas of cube 1 to cube 2 = 150:96.
= 25:16

Thus, the required ratio of area of cubes is 25 : 16.  

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Final answer:

The value of m – n when m = –2.6 and n = 7.9 is –10.5, which is an option (a).

Explanation:

To evaluate m – n when m = –2.6 and n = 7.9, we simply substitute the given values into the expression and perform the subtraction:

m – n = –2.6 – 7.9

Since subtracting a positive number is the same as adding its negative, this is equivalent to:

m – n = –2.6 + (–7.9)

Adding these two negative numbers together gives us:

m – n = –10.5

Therefore, the correct answer is a. –10.5.

The correct statement is:

We know that the general form of a slope intercept form of a line is given by:

[tex]y=mx+c[/tex]

where m is the slope of the line and c is the y-intercept of a line.

The function f(x) is given by:

[tex]f(x)=-2x-1[/tex]

Hence, on comparing the function to the slope-intercept form of a line we get

The y-intercept of function f(x) is: -1

Also, the table for the function g(x) is given by:

         x           g(x)

         2            2

         4            6

         6           10

The function g(x) satisfies the equation:

[tex]g(x)=2x-2[/tex]

The y-intercept of the function g(x) is: -2

Since we know that:

  -1 > -2

This means that the y-intercept of the function f(x) is higher than the y-intercept of the function g(x).

The two pairs of polar coordinates are :  [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]

Polar coordinates are coordinates  labeled as ( r, θ ) , where r = radial coordinate while θ is known as the angular coordinate. Polar coordinates are also plotted on a polar grid.

Using the given data

Point ( 3 , - 3 )

[tex]r = \sqrt{3^2 + (-3)^2} = 3\sqrt{2}[/tex]

θ =

[tex]tan^{-1} (\frac{-3}{3}) = \pi - \frac{\pi }{4} , 2\pi - \frac{\pi }{4} \\\\= 3\pi , \frac{7\pi }{4} , -\frac{\pi }{4}[/tex]

In degrees = 135° , 315° , -45° ( neglecting  -45° )

Hence the two pairs of polar coordinates for the point ( 3 , -3 )  can be taken  as ;  [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]

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Answer:

c on edge

Step-by-step explanation:

Answer:

The answer is the table B

Step-by-step explanation:

we have

[tex]f(x)=2x^{3}-26x-24[/tex]

Using a graphing tool

see the attached figure to better understand the problem

Relation of graph to the x-axis

Interval (-∞,-3) -----> below (the function is negative)

Interval (-3,-1) -----> above (the function is positive)

Interval (-1,4) -----> below (the function is negative)

Interval (4,∞) ----->above (the function is positive)

To convert the exponential equation 4c = 256 into a logarithmic form, one can apply the logarithm to both sides, simplifying using the property that the logarithm of a power is the exponent times the logarithm of the base, yielding the equivalent equation c = 4.

The question requires us to convert the exponential equation 4c = 256 into a logarithmic form. To achieve this, we need to recognize that a logarithm function is the inverse of an exponential function. Therefore, applying a logarithm to both sides of the equation will allow us to solve for the variable c.

It's important to note that any logarithmic base can be used, but common practice is to use either base 10 (common logarithm) or the natural base e (natural logarithm).

Since 256 is 4 raised to the 4th power (4⁴), we can write the equation as 4c = 4⁴. By applying the logarithm, we then get the equivalent logarithmic equation log(4c) = log(4⁴).

Using the property of logarithms that states the logarithm of a number raised to an exponent will be the product of the exponent and the logarithm of the number, we can simplify this to c*log(4) = 4*log(4). Since log(4) is a common factor on both sides, dividing by log(4) gives us c = 4.

Final answer:

This detailed answer explains the probability of selecting a heart or a face card from a standard deck of cards and the calculation involved.

Explanation:

Calculate the probability of selecting a heart or a face card from a standard deck of cards:

By the principle of inclusion-exclusion, you add the probabilities of selecting a heart and a face card and subtract the probability of both (heart face cards, which are only the face cards that are hearts - 3 cards):

(1/4) + (3/13) - (3/52) = 39/52 = 3/4

since the last number -s -20 you need the 2 that when multiplied together would equal -20

 so x-5 and x +4 are the correct answers

Step-by-step explanation:

Please find the attachment of graph representing the axis of symmetry.

We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:

[tex]f(x)=(x-2)^2+1[/tex]

We can see that our function represents a parabola.

Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.

Let us find the vertex of our given parabola using formula: [tex]x=\frac{-b}{2a}[/tex], where,

a = Coefficient of [tex]x^{2}.[/tex]

b = Coefficient of x.

To apply this formula we will represent our parabola as a quadratic equation [tex](ax^2+bx+c)[/tex] as:

[tex]f(x)=x^2-4x+4+1[/tex]

[tex]f(x)=x^2-4x+5[/tex]  

Upon substituting a= 1 and b= -4 in the formula we will get,

[tex]x=\frac{-(-4)}{2*1}[/tex]

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

[tex]x=2[/tex]  

Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.

Factoring Polynomials with Four Terms, and Factoring Trinomials by Grouping can be used to rewrite square trinomials and difference of squares binomials as separate factors