Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x.

Identify and interpret the slope in this scenario.

a. The slope is −4.0. Starting at 0.5, the GPA will decrease by 4.0 for every text sent in class.
b. The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.
c. The slope is 4.0. Starting at 0.5, the GPA will increase by 4.0 for every text sent in class.
d. The slope is 0.5. Starting at 4.0, the GPA will increase by 0.5 for every text sent in class.

Answer:

Josh has 29 coins.

Step-by-step explanation:

Let Terry have x coins then Josh has x + 12 coins.

Together they have x + x + 12 coins so we can form the equation:

x + x + 12 = 46

2x + 12 = 46

2x = 46 - 12 = 34

x = 17, so Terry has 17 coins and Josh has 17 + 12 = 29 coins.

Answer:

23

Step-by-step explanation:

f(x)=3 − 4x

Let x=-5

f(-5) = 3-4(-5)

       = 3 -(-20)

      = 3+20

     =23

Answer:

17mL

Step-by-step explanation:

Convert 0.85 gr to miligrams

If 100 mg is 1 gr. Then, 0.85 gr is 850 mg

So, 850 multiply for 5ml and divide for 250 ml

or [tex]850mg  \frac{5ml}{250mg}[/tex]

So all mg is gone and the amount of mililiters is 17

Answer:

17 milliliters of dose should be poured into a prescription bottle.

Step-by-step explanation:

Amount of dose in liquid antiboitic = 0.85 g = 850 mg

1 g = 1000 mg

Concentration of antibiotic = 250 mg/5 ml = 50 mg/mL

So, in 1 mL of liquid we have 50 mg of antibiotic.

Then in 0.85 mg of antibiotic will be:

[tex]\frac{1}{50}\times 850 mL=17 mL[/tex]

17 milliliters of dose should be poured into a prescription bottle.

Answer:

y=-5x-58

Step-by-step explanation:

The equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Perpendicular lines have opposite reciprocal slopes.

Anyways we need to find the slope of the line going through (10,6) and (5,5).

To find the slope, we are going to line up the points vertically and subtract vertically, then put 2nd difference over 1st difference. Like so:

 (  10   ,   6)

- (   5   ,   5)

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

    5         1

So the slope of the line through (10,6) and (5,5) is 1/5.

The slope of a line that is perpendicular will be the opposite reciprocal of 1/5.

The opposite reciprocal of 1/5 is -5.

The line we are looking for is y=-5x+b where we need to find the y-intercept b.

y=-5x+b goes through (-10,-8)

So we can use (x,y)=(-10,-8) to find b in y=-5x+b.

y=-5x+b with (x,y)=(-10,-8)

-8=-5(-10)+b

-8=50+b

Subtract 50 on both sides:

-8-50=b

-58=b

So the equation is y=-5x-58

Answer:

24 students

Step-by-step explanation:

So we started with 32 cups of juice.

Kahled drunk 2 cups so (32-2)=30 cups is left.

If x represents the number of students he receive juice and each student gets the same amount of juice which is 1.25 cups, then we have the equation

1.25x=30 to solve for x.

Divide both sides by 1.25:

x=30/1.25

x=24

24 students receive juice

Answer:

Part 1) [tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

cosine theta equals plus or minus square root of seven over 4

Part 2) [tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]

tangent theta equals plus or minus three over square root of seven

or

[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]

tangent theta equals plus or minus three times square root of seven over seven

Step-by-step explanation:

we have that

The sine of angle theta is equal to

[tex]sin(\theta)=\frac{3}{4}[/tex]

Is positive

therefore

The angle theta lie on the I Quadrant or in the II Quadrant

Part 1) Find the value of the cosine of angle theta

Remember that

[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]

we have

[tex]sin(\theta)=\frac{3}{4}[/tex]

substitute and solve for cosine of angle theta

[tex](\frac{3}{4})^{2}+cos^{2} (\theta)=1[/tex]

[tex]cos^{2} (\theta)=1-(\frac{3}{4})^{2}[/tex]

[tex]cos^{2} (\theta)=1-\frac{9}{16}[/tex]

[tex]cos^{2} (\theta)=\frac{7}{16}[/tex]

[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

cosine theta equals plus or minus square root of seven over 4

Part 2) Find the value of tangent of angle theta

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

we have

[tex]sin(\theta)=\frac{3}{4}[/tex]

[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

substitute

[tex]tan(\theta)=\frac{\frac{3}{4}}{(+/-)\frac{\sqrt{7}}{4}}[/tex]

[tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]

tangent theta equals plus or minus three over square root of seven

Simplify

[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]

tangent theta equals plus or minus three times square root of seven over seven

The correct values for cosine and tangent when sine theta equals 3/4 are, cosine theta equals plus or minus 3/4, and tangent theta equals plus or minus 3/7. These values are found using the Pythagorean identity and the definitions of tangent in terms of sine and cosine.

To solve for cos θ and tan θ when given that sin θ = ¾, one can use the Pythagorean identity, which states that sin2 θ + cos2 θ = 1. Substituting the known value of sin θ, we get (¾)2 + cos2 θ = 1. Solving this equation yields cos2 θ = 1 - (¾)2 = ¹⁄16, so cos θ is either the positive square root of ¹⁄16 or its negative counterpart. Since the square root of ¹⁄16 is ³⁄4, cos θ can be either ³⁄4 or -³⁄4.

For tan θ, which is defined as sin θ/cos θ, we use the positive and negative values found for cos θ. Therefore, tan θ can be 3/4 divided by ³⁄4, which simplifies to ³⁄7 or, when using the negative cosine value, tan θ will be -³⁄7.

Answer:

A

Step-by-step explanation:

A translation of 6 units down means subtract 6 from the original y- coordinates while the x- coordinates remain unchanged, that is

(4, 2 ) → (4, 2 - 6 ) → (4, - 4 )

(- 2, 2 ) → (- 2, 2 - 6 ) → (- 2, - 4 )

Answer:

4i

Step-by-step explanation:

sqrt(-16)

We know the sqrt (ab) = sqrt(a) sqrt(b)

sqrt(-16) = sqrt(16) sqrt(-1)

We know that the sqrt(-1) = i

             = 4i

Answer:

4i

Step-by-step explanation:

sqrt(-16)

We know the sqrt (ab) = sqrt(a) sqrt(b)

sqrt(-16) = sqrt(16) sqrt(-1)

We know that the sqrt(-1) = i

            = 4i

Answer:

The answer is C

Step-by-step explanation:

Use the method of elimination

First rearrange the first equation to look like the second

[tex]2x + 3y = 17 \\ 4x + 6y = 34 \\ - 4x - 6y = - 34[/tex]

Next add the two equations together eliminating the y term.

[tex] - 4x - 6y = - 34 \\ 3x + 6y = 30 \\ \\ - x = - 4 \\ x = 4[/tex]

There's only one answer with x = 4 so you're done. To go further, substitute x = 4 into the second equation and solve for y

[tex]3x + 6y = 30 \\ 3 \times 4 + 6y = 30 \\ 12 + 6y = 30 \\ 6y = 18 \\ y = 3[/tex]

Answer:

c

Step-by-step explanation:

Answer:

-5x+13 given (-x+3)-(4x-10)

Answer:-5x+13

Step-by-step explanation:

We are going to distribute to get rid of the ( ):

-x+3-4x+10

Pair up like terms:

-x-4x+3+10

Combine the like terms:

-5x+13

Answer:

-5x+13

Step-by-step explanation:

( - x + 3) - (4x - 10)

Distribute the minus sign

( - x + 3) - 4x + 10

Combine like terms

-5x +13

The ratio you need to find is goals : games

In this case you have...

9 goals

12 games

Plug this into the ratio goal : games

9 : 12

This ratio can be further reduced to...

3 : 4

What this means in words:

A hockey player will make 3 goals for every 4 games

Hope this helped!

~Just a girl in love with Shawn Mendes

Finding limits by direct substitution means simply means to evaluate the function at the desired value: in the first case, we have to evaluate [tex]f(x)=x^2-3[/tex] at [tex]x=0[/tex]: we have

[tex]f(0)=0^2-3 = 0-3=-3[/tex]

Similarly, in the second example, we have

[tex]f(x)=x^2+3x-1 \implies f(3) = 3^2+3\cdot 3-1 = 9+9-1 = 17[/tex]

Going on, we have

[tex]f(x) = \dfrac{x^2-16}{x-4} = \dfrac{(x+4)(x-4)}{x-4} = x+4[/tex]

And thus we have

[tex]f(4) = 4+4=8[/tex]

Finally, we have

[tex]f(x) = \dfrac{x^2-2x}{x^4} = \dfrac{x(x-2)}{x^4} = \dfrac{x-2}{x^3}[/tex]

So, we can't evaluate this function at 0.

The limits of the functions are determined and the values are:

5) -3

6) 17

7) 8

8) does not exist.

Given data:

5)

The limit function is expressed as  [tex]\lim_{x \to 0} (x^{2} -3)[/tex].

So, when x = 0, the limit is:

L = 0² - 3

L = -3

6)

The limit function is expressed as  [tex]\lim_{x \to 3} (x^{2} +3x - 1)[/tex].

So, when x = 3, the limit is:

L = 3² + 3 ( 3 ) - 1

L = 9 + 9 - 1

L = 17

7)

The limit function is expressed as  [tex]\lim_{x \to 4} \frac{(x^{2} -16)}{x-4}[/tex].

So, when x = 4, the limit is simplified as:

[tex]\lim_{x \to 4} \frac{(x^{2} -16)}{x-4}=\lim_{x \to 4} \frac{(x-4)(x+4)}{x-4}[/tex]

[tex]\lim_{x \to 4} \frac{(x-4)(x+4)}{x-4}=\lim_{x \to 4} (x+4)[/tex]

L = 4 + 4

L = 8

8)

The limit function is expressed as  [tex]\lim_{x \to 0} \frac{(x^{2} -2x)}{x^{4} }[/tex].

So, when x = 0, the limit is simplified as:

L = 0/0 and the limit does not exist.

Hence, the limits are solved.

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Answer:

C

Step-by-step explanation:

When both the numerator and denominator of a rational function have the same degree, you divide the highest powered term's coefficients. That is the horizontal asymptote.

Since this function has third degree in both the numerator and denominator, we divide the respective coefficients to find the horizontal asymptote.

So, y = 9/7

Correct answer is C

Note:  horizontal asymptote is always in the form y = a (where a is the constant)

Answer:

0.012

Step-by-step explanation:

The probability of more than 7 customers arriving within a minute is obtained by taking the probability at X equal to 0, 1, 2, 3, 4, 5, 6, and 7 then subtracting from the total probability. It can be expected about 1.2% of times that more than 7 customers arriving within a minute.

Answer: 0.0216

Step-by-step explanation:

Given : Average arrivals of customers at a local grocery store = 3 per minute

The Poisson distribution formula :-

[tex]\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where [tex]\lambda[/tex] is the mean of the distribution.

If X = the number of arrivals per minute, then the probability of more than 7 customers arriving within a minute will be :-

[tex]\dfrac{e^{-3}(3)^7}{7!}=0.0216040314525\approx0.0216[/tex]

Hence, the probability of more than 7 customers arriving within a minute = 0.0216

Answer: 34 miles

Step-by-step explanation:

First multiply the 2 miles she power walked by the 7 days. (14 miles)

Next, multiply the 5 miles by the 4 days. (20)

Add both numbers, 20+14=34 miles

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=56\ m,\ hypotenuse=65\ m,\ leg=x\ m[/tex]

Substitute:

[tex]56^2+x^2=65^2[/tex]

[tex]3136+x^2=4225[/tex]          subtract 3136 from both sides

[tex]x^2=1089\to x=\sqrt{1089}\\\\x=33\ m[/tex]

Answer:

33

Step-by-step explanation:

We need to use the Pythagorean Theorem.

65 is the length for the hypotenuse.

So we do a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.

x^2+56^2=65^2

x^2+3136=4225

Subtract 3136 on both sides

x^2         =1089

Square root both sides

x=33

The answer is 33 meters.

thats easy it is 4

Hope this helps:)

Answer:

79.67479675 %

Step-by-step explanation:

To find the percentage take the correct amount over the total amount, then multiply by 100

98/123 * 100

79.67479675 %

Answer:

the answer is 79.64%

Step-by-step explanation:

A/B=P/100

98/123=p/100

9800/123=123p/123

p=79.64%

Answer:

C

Step-by-step explanation:

The absolute value function always returns a positive value

However, the expression inside the bars can be positive or negative

| 3 | = 3 and | - 3 | = 3, hence the solution of

| x | = 3 is x = ± 3

Extending this to

| x² - 4 | = 3, then

| x² - 4 | = 3 and | - (x² - 4) | = 3

x² - 4 = 3 ; - (x² - 4) = 3 → C

Answer:

C

Step-by-step explanation:

[tex]|x^2-4|=3[/tex]

Before we say what this implies, we need to know that |-1|=1 and |1|=1.

So what I'm saying is:

[tex]|-(x^2-4)|=|-1 \cdot (x^2-4)|=|-1| \cdot |x^2-4|[/tex]

[tex]=|x^2-4|[/tex].

So [tex]|x^2-4|=3[/tex] implies:

[tex](x^2-4)=3[/tex] or [tex]-(x^2-4)=3[/tex].

Answer:

x=-1 or x=3

Step-by-step explanation:

This is a quadratic equation

You can use the graph tool to visualize the x-intercepts on the graph as attached below.

x=-1 or x=3

For this case we must find the x-intersepts values of the following equation:

 [tex]y = -4x ^ 2 + 8x + 12[/tex]

Doing y = 0 we have:

[tex]0 = -4x ^ 2 + 8x + 12[/tex]

Dividing between -4 on both sides of the equation:

[tex]x ^ 2-2x-3 = 0[/tex]

We factor, we look for two numbers that when multiplied by -3 and when added by -2. These are -3 and 1:

[tex]-3 + 1 = -2\\-3 * 1 = -3\\(x-3) (x + 1) = 0[/tex]

Thus, the x-intercepts values are:

[tex]x_ {1} = 3\\x_ {2} = - 1[/tex]

Answer:

[tex]x_ {1} = 3\\x_ {2} = - 1[/tex]

Answer:

Step-by-step explanation:

[tex]f(x)=\left\{\begin{array}{ccc}x+4&if&-4\leq x<3\\2x-1&if&3\leq x<6\end{array}\right\\\\\text{The domain of a function is a set of x's}.\\\\\text{We have}\\\\-4\leq x<3\to x\in[-4,\ 3)\\3\leq x<6\to x\in[3,\ 6)\\\\\text{The domain:}\ [-4,\ 3)\ \cup\ [3,\ 6)=[-4,\ 6)[/tex]

Answer: I believe the answer is B.

Although, if the answer to this question isn't B, it should defiantly be C.

Answer:

The correct option is B.

Step-by-step explanation:

The graph of f(x) is g(x) is given.

Graph of both functions intersect each other at a point. Before the point of intersection g(x)>f(x) and after the point of intersection g(x)<f(x).

The graph of f(x) will eventually exceed the graph of g(x). Therefore the correct option is B.

Function g(x)<f(x) for the large value of x, So option A is incorrect.

From the given graph it is clear that the y-intercept of f(x) is 0.2 and y-intercept of g(x) is 2.

So, option C and D are incorrect.

Answer:

[tex]\large\boxed{x=\dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]4^{(4x-1)}=32\\\\(2^2)^{4x-1}=2^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-1)}=2^5\iff2(4x-1)=5\ \ \text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(4x)+(2)(-1)=5\\\\8x-2=5\qquad\text{add 2 to both sides}\\\\8x=7\qquad\text{divide both sides by 8}\\\\x=\dfrac{7}{8}[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+2y=14\\-x+y=5&\text{\underline{multiply both sides by 2}}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}2x+2y=14\\-2x+2y=10\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=24\qquad\text{divide both sides by 4}\\.\qquad\qquad y=6\\\\\text{put the value of y to the second equation:}\\\\-x+6=5\qquad\text{subtract 6 from both sides}\\-x=-1\qquad\text{change the signs}\\x=1[/tex]

Answer: Its Multiplication property of Equality

Step-by-step explanation: Just did the test

Answer:

Piston displacement = 84.8

Step-by-step explanation:

We will find the volume of the cylinder in order to find the piston displacement.

Here, (bore = diameter, so r = diameter/2) (height = stroke)

Volume = [tex] \pi r^2h[/tex] [tex]=3.14\times1.5^2\times 3[/tex] = 21.2 cubic units

Since the engine has 4 cylinders, so we will multiply the piston displacement by 4 to get:

Piston displacement = [tex]21.2 \times 4[/tex] = 84.8

The total piston displacement for a 4-cylinder engine with a bore and stroke of 3 inches can be calculated using the formula: pi/4 * bore^2 * stroke * number of cylinders. For this example, it is approximately 113.097 cubic inches.

To calculate the total piston displacement, we use the formula for the displacement of a single cylinder, which is pi/4 * bore^2 * stroke * number of cylinders.

In this scenario, the bore and stroke are both 3 inches and it's a 4-cylinder engine. Therefore, we plug in these values into the formula.

So, the total displacement is pi/4 * (3inch)^2 * 3inch * 4. This calculates to approximately 113.097 cubic inches.

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Answer:

5 x 2 = 10

(10^20)^5 = 10^100

(10) x (10^100) = 10^101 which is 1 followed by 101 zeroes.

Answer:

10 ^101

Step-by-step explanation:

(5 x 2)(10^20)^5

5*2 = 10

We know a^b^c = a^(b*c)

(10^20)^5 = 10 ^ (20*5) = 10 ^ 100

10 * 10^100

Replacing 10 with 10^1

10^1 * 10^100

We know that a^b * a^c = a^ (b+c)

10^1 * 10^100 = 10 ^(100+1) = 10 ^101

Answer:

r = 4.2 cm; d = 8.4 cm

Step-by-step explanation:

The radius is the distance from the centre of the circle to the circumference.

r = 4.2 cm

The diameter is the length of a straight line that passes through the centre with each end at the circumference.

d = 2r = 2 × 4.2 cm = 8.4 cm

Answer:

radius=4.2

diameter=8.4

Step-by-step explanation:

Answer:

r= 9

Step-by-step explanation:

;/

The solution to the equation 21 + 3r = 48 is r = 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3x + 5 = 9 is an equation.

We have,

21 + 3r = 48

Subtract 21 on both sides.

3r = 48 - 21

3r = 27

Divide both sides b 3.

r = 9

Thus,

The value of r is 9.

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Answer:

C) not isomeric because side lengths not same

Step-by-step explanation:

Isometric means that the lengths are preserved after rotation or transformation.

As we can see in the given figures that the lengths of sides of the original figure and transformed figure are are not same which means the lengths are not preserved.

So the correct answer is:

C) not isomeric because side lengths not same ..

Option: C is the correct answer.

C)   Not isomeric because side lengths not same.

Isometry--

It is a transformation which preserves the length of  the original figure i.e. it is a distance preserving transformation.

Two figures are said to be isometric if they are congruent.

By looking at the figure displaying the transformation we observe that the size of the original figure is changed.

i.e. the figure is dilated by a scale factor of 2 , since each of the sides of the polygon which is a trapezoid is increased by a factor of 2.

Hence, the transformation is not an isometry.

Answer:

Option D is correct.

Step-by-step explanation:

We need to find that how many quarts are there in 583.7 liters.

From conversion table we geet,

1 quart = 0.95 liters

=> 1 liters = 1/0.95 quarts

=> 1 liters = 1.0526 quarts

I liter has 1.0526 quarts then 583.7 liters will have:

583.7 liters = 1.0526*583.7 quarts

583.7 liters = 614,4 quarts.

So, Option D There are 614.4 quarts in 583.7 liters. is correct.

Answer:

d

Step-by-step explanation: