Write the equation of each line in slope-intercept form
(If possible, please show work)

Answer:

20°

Step-by-step explanation:

A complementary angle adds up to 90°. If the other angle is already 70°, then the missing angle that adds up would have to be 20°

Answer:

20

Step-by-step explanation:

Complementary angles add up to 90°.

90 - 70 = 20

The measure of the complementary angle is 20°.

Answer:

Step-by-step explanation:Josh

By comparing the given numbers, Jhon had most money.

As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.

The rules of the ordering and the comparing of the integers are given below:

Given that, John had $800 Tasha has $500 Kyle had $300.

Here, 300<500<800

Therefore, by comparing the given numbers, Jhon had most money.

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Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

a) The probability of obtaining a sample mean that is less than or equal to 1770 hours is P(M≤1770)=0.0013.

b) It is unusual, as there are only 13 chances in 10,000 (0.13%) of having this outcome.

Step-by-step explanation:

We have a population lifetime with mean of 1800 hours and standard deviation of 100 hours.

Samples of size n=100 are taken and tested.

We can calculate the probability of obtaining a sample mean that is less than or equal to 1770 hours using a z-score for the sample Mean M=1770 and then calculating its probability according to the standard normal distribution:

[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1770-1800}{100/\sqrt{100}}=\dfrac{-30}{10}=-3\\\\\\P(X<1770)=P(z<-3)=0.0013[/tex]

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

36 ft²

Step-by-step explanation:

Split the figure into two shapes.

Area of figure = Area of rectangle + Area of triangle

Area of rectangle:

[tex]length \times width[/tex]

[tex]length=8\\width=4[/tex]

[tex]8 \times 4 = 32[/tex]

Area of triangle:

[tex]\frac{base \times height}{2}[/tex]

[tex]base=8-4=4\\height=2[/tex]

[tex]\frac{4 \times 2}{2}[/tex]

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

Area of figure = [tex]32 + 4 = 36[/tex]

Answer:

Option C is the correct option.

Step-by-step explanation:

Solution,

Height = 2 ft

Base = 8 - 4 = 4 ft

Finding the area of ∆ ABC :

[tex] \frac{1}{2} \times b \times h[/tex]

[tex] = \frac{1}{2} \times 4 \times 2[/tex]

[tex] = 4 \: {ft}^{2} [/tex]

Finding the area of rectangle BDEF:

[tex]length \: \times breadth[/tex]

[tex] = 8 \times 4[/tex]

[tex] = 32 \: {ft}^{2} [/tex]

Total area :

Area of triangle ∆ABC + Area of rectangle BDEF

[tex] = 4 \: {ft}^{2} + 32 { \: ft}^{2} [/tex]

[tex] = 36 \: {ft}^{2} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

25, 55, 100

Step-by-step explanation:

Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:

x + x + 30 + 4x = 180

6x + 30 = 180

6x = 150

x = 25°

x + 30 = 25 + 30 = 55°

4x = 25 * 4 = 100°

The sum of angles is 180.

[tex] \alpha + \beta + \gamma = 180 [/tex]

[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]

[tex]6 \alpha = 150[/tex]

[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]

Answer: C) 40 degrees

Step-by-step explanation:

if the total angle is 70 degrees and part of it is 30 degrees

then the other part is x degrees

30 + x = 70

30 - 30 + x = 70 - 30

x= 40

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Answer:

trapezoid

Step-by-step explanation:

FXYH is trapezoid with two parallel bases XY and FH.

Answer:

24

Step-by-step explanation:

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), we get:

[tex]32+3(6-22)/6=\\32+3(-16)/6=\\32-48/6=\\32-8=\\24[/tex]

Answer:

24

Step-by-step explanation:

32 + 3(6 − 22) ÷ 6

PEMDAS

Parentheses first

32 + 3(-16) ÷ 6

Multiply and divide from left to right

32+ -48÷ 6

32+ -8

Then add and subtract from left to right

24

Answer:

y = 2x - 6

Explanation:

* note

the equation provided is written in standard form.

· standard form → Ax + By = C

· slope-intercept form → y = mx + b

To convert the given equation to slope-intercept form, start by subtracting '2x' from both sides of the equation. This will move 'y' to the left side of the equation.

2x - y = 6

2x - 2x - y = 6 - 2x

-y = -2x + 6

Next, multiply both sides of the equation by negative one.

-y = -2x + 6

(-y × -1) = (-2x × -1) + (6 × -1)

y = 2x - 6

Therefore, the given equation should be y = 2x - 6 when converted to slope-intercept form.

The equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

Given is an equation of a line we need to convert it into slope-intercept form,

To convert the equation 2x - y = 6 to slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the "y" variable on one side of the equation.

Starting with the given equation:

2x - y = 6

Move the 2x term to the right side by adding "y" to both sides:

2x = y + 6

Rearrange the equation by swapping the sides:

y + 6 = 2x

Move the constant term (6) to the right side by subtracting 6 from both sides:

y = 2x - 6

Hence the equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

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Answer: A

Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Answer:

A

Step-by-step explanation:

f(x) = x² + 3x + 5

Substitute x value with (a+ h)

f(a+h) = (a+h)² + 3(a+h) + 5

         = a² +2ah +h² + 3a + 3h + 5

Answer:  If the sum of the measures of two angles is not 90°, then they  are not complementary angles.

Step-by-step explanation:

Contrapositive of p → q    is    ~q → ~p  where p is the hypothesis and q is the conclusion.

Hypothesis (p) = Two angles are complementary

                  ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°

                  ~q = The sum of their measures is not 90°

~ p → ~q = If the sum of the measures of two angles is not 90°,

                then they are not complementary angles.

If the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

These are statements that negates the given statement:

Given the statement; If two angles are complementary, then the sum of their measures is 90

Hypothesis (p) = Two angles are complementary  

                 ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°  

                 ~q = The sum of their measures is not 90°

Hence the  statement that is the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

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Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=50-1=49[/tex]

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]

The 95% confidence interval for the mean is (5.73, 6.95).

Answer:

-61.5°C

Step-by-step explanation:

Answer:

-61.5 cell

Step-by-step explanation:

Answer:

Answer B, 123 degrees

Step-by-step explanation:

Angle 3 and angle 6 are alternate interior angles. This means that, by the Alternate Interior Angles Theorem, they are congruent, and therefore equal.

The pair of angles created on the inner side of the parallel lines but on opposing sides of the transversal is known as an alternative interior angle. The measure of ∠6 is 123°.

When two parallel lines are intersected by a transversal, the pair of angles created on the inner side of the parallel lines but on opposing sides of the transversal is known as an alternative interior angle. These angles are always equal in measure.

Given that a bridge crosses over the Madison River. The opposite banks of the river are parallel and the bridge is a transversal. Therefore, the measure of the ∠3 and ∠6 will be equal. This is because the two angle are alternate interior angles.

Thus, the measure of ∠6 i,

∠6 = ∠3 = 123°

∠6 = 123°

Hence, the measure of ∠6 is 123°.

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Answer:

18

Step-by-step explanation:

Answer: -12

Step-by-step explanation:

1/4x + 1/3x = x + 5

7/12 x = x + 5

7x = 12(x+5)

7x = 12x +5

x = -12

Answer:

F(x) = 3x^2

Step-by-step explanation:

The other equations have other things in the equation. Those other stuff will shift the parabola so thats how you know.

Answer:

4095

Step-by-step explanation:

3(4⁰) + 3(4¹) + 3(4²) + 3(4³) + 3(4⁴) + 3(4⁵)

3(4⁰ + 4¹ + 4² + 4³ + 4⁴ + 4⁵)

3(1 + 4 + 16 + 64 + 256 + 1024)

3 * 1365 = 4095

Answer:

4095

Step-by-step explanation:

3(4ⁿ⁻¹),

r= 4,

n=6

S₆=?

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

3*(4⁰+4¹+4²+4³+4⁴+4⁵)= 3*(4⁶-1)/(4-1)= 4095

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

Answer: The integers are 7 and 14.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2

Substitute equation 1 into 2

[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]

Find the LCM of 2y and y

[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]

Substitute y = 7 into equation 1:

Recall that x = 2y

[tex]x = 2(7)\\x = 14[/tex]

Hence the required two integers are 7 and 14.

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Answer:

y = 5x - 4

Step-by-step explanation:

Step 1: Write known variables

m = 5

y = 5x + b

Step 2: Find b

6 = 5(2) + b

6 = 10 + b

b = -4

Step 3: Rewrite equation

y = 5x - 4

Answer:

  Every point is moved so that it is 2/3 as far from the y-axis

Step-by-step explanation:

Translation and reflection are "rigid" motions. They do not change the size or shape of the figure, so the resulting figure will be congruent with the original.

Dilation by a factor of 2/3 changes the size, so will not result in a congruent figure.

_____

Here the dilation is in the x-direction only. It is not a transformation we usually are interested in.

Answer:

 Every point is moved so that it is 2/3 as far from the y-axis

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose you are forming a committee from a group of 15 biology student, 12 math students, and 9 physics students. How many possibilities are there if your committee needs to have at most 2 biology students, exactly 3 math students, and exactly 2 physics students?

To tackle this question, we will use the concept of combination since it deals with selection. Generally, selecting 'r' objects out of 'n' pools of object can be done using the formula;

nCr = n!/(n-r)!r!

If we are to form a committee of at most 2 biology students, exactly 3 math students and exactly 2 physics students from a group of 15 biology student, 12 math students, and 9 physics students, this can be done in the following ways;

For Physics students:

Selecting exactly 2 physics students from a group of 9 students will be:

9C2 = [tex]\frac{9!}{(9-2)!2!}\\[/tex]

= [tex]\frac{9!}{(7)!2!}\\[/tex]

[tex]= \frac{9*8*7!!}{(7)!2!}\\= 9*4\\= 36ways[/tex]

for Mathematics students:

Selecting exactly 3 math students from a group of 12 students will be:

[tex]12C3 = \frac{12!}{12-3)!3!}\\= \frac{12!}{9!3!}\\= \frac{12*11*10*9!}{9!*6}\\= 220 ways[/tex]

For Biology Students:

Selecting at most 2 biology students from a group of 15biology student will be:

15C1 * 15C2 (at most 2 students)

= [tex]\frac{15!}{14!1!} * \frac{15!}{13!2!}\\\\[/tex]

= 15*105

= 1,575 ways

The total number of possibilities will be = 36*220*1,575 = 12,474,000 possibilities

Answer:3x^3y^2(the third option) is the correct answer

Hope this helped!

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Answer:

True

Step-by-step explanation:

The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.

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▹ Answer

V ≈ 160.22

▹ Step-by-Step Explanation

V = πr²[tex]\frac{h}{3}[/tex]

V = π3²[tex]\frac{17}{3}[/tex]

V ≈ 160.22

Hope this helps!

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