A linear function has a slope of -7 /9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = -7/9 (x minus 18)?

Answer:

AP = 14

Step-by-step explanation:

According to secant-secant theorem

(CP)(PD)=(BP)(AP)

7×12=6×AP

AP = 84/6

AP = 14

Answer:

5 filters

Step-by-step explanation:

1 filter = 1 million remain

2 filter =100,000 remain

3 filter =10,000 remain

4 filter =1,000 remain

5 filter  = 100 remain which is below to 500

To reduce the pollutant to below 500 particles per gallon, the water would need to be filtered through 13 filters.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Let's first define a variable, p, to represent the number of filters. We can then say that the number of particles remaining in the water after the first filter is applied is 0.9 x 10,000,000 = 9,000,000 particles per gallon.

After the second filter is applied, the number of particles remaining is 0.9 x 9,000,000 = 8,100,000 particles per gallon, and so on.

This equation would be [tex]0.9^p \times 10,000,000[/tex]. We want to find the smallest value of p that makes this expression less than 500.

We can solve this by setting the expression equal to 500 and solving for p. This gives us the equation [tex]0.9^p \times 10,000,000=500[/tex].

Solving for p, we get p = log(500/10,000,000) / log(0.9), which is approximately 12.39.

Since we can only use a whole number of filters,

Thus, we would need to use 13 filters to reduce the pollutant to below 500 particles per gallon.

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Answer:

Shen has a slower heart rate than Adrian.

Shen’s unit heart rate is 64 beats per minute.

Adrian’s unit heart rate is 72 beats per minute.

Answer:

36

Step-by-step explanation:

In circle with center O,

[tex] chord\overline {EF} \cong chord\overline {WV}... (Given) [/tex]

Since, congruent chords are equidistant from the center of the circle.

[tex] \therefore PG = GO\\

\therefore - x +10 = - 3(x+2)\\

\therefore - x + 10 = - 3x - 6\\

\therefore 3x - x = - 6-10\\

\therefore 2x = - 16\\\\

\therefore x = \frac{-16}{2} \\\\

\huge \red {\boxed {\therefore x = - 8}} \\\\

\because \overline {PO} = \overline {PG} + \overline {GO} \\

\therefore \overline {PO} = - x + 10 + \{-3(x + 2)\}\\

\therefore \overline {PO} = - x + 10 - 3x - 6\\

\therefore \overline {PO} = - 4x + 4 \\

\therefore \overline {PO} = - 4\times (-8)+ 4 \\

\therefore \overline {PO} =32+ 4 \\

\huge \orange {\boxed {\therefore \overline {PO} =36}} \\[/tex]

Answer:

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Step-by-step explanation:

To find the experimental probability of an outcome we divide:

The number of trials in which the desired outcome happened by the total number of trials.

In this question:

Experimental probability of winning this game.

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Answer: A=286.2 m²

Step-by-step explanation:

The surface area of a cone is [tex]A=\pi r(r+\sqrt{h^2+r^2} )[/tex].

We are given h=11 m and r=5 m. With these values, we can plug them into the equation to find the surface area.

[tex]A=\pi (5)(5+\sqrt{11^2+5^2} )[/tex]

[tex]A=5\pi (5+\sqrt{146} )\\[/tex]

[tex]A= 268.2 m^2[/tex]

Answer:

The cone pictured has a surface area of_268.2___a0 square meters

Step-by-step explanation:

SA of a cone = πr² + πrs

s = slant height

s = √h² +r²

so combined together

SA of a cone = πr² + πr(√h² + r²) = πr(r +√h² + r²)

SA of a cone = 3.14*5(5+[tex]\sqrt{11^{2}+ 5^{2} }[/tex] ) =268.2038

Answer:

Step-by-step explanation:

Given that:

An epidemiologist found five cases of "big toe cancer" in the Yukon Territory.

Therefore, shoe size > 9

1) From the required data given below

                       Case       Control       Total

Yes                2(a)             3(b)            5

No                  3(c)             2(d)            5

Total               5                 5                10

∴ odds ratio = ad/bc

= 4/9

=0.444

2) From the less than 1.0 mean that the odds of cancer among case is lower than the odds of cancer among controls

Answer:

Matt ran 6 miles.

Step-by-step explanation:

Stan ran 4 and 7/10 miles, and this is 1 and 3/10 fewer miles than Matt.

this means that Matt ran the following amount of miles

4 and 7/|0 + 1 and 3/10 miles:

(4 + 1) + (7/10 + 3/10) = 5 + 10/10 = 6 miles.

This would be the correct way to solve this equation.

Answer:

70°

Step-by-step explanation:

Since it's a trapezoid the sum of a and x would be 180°

110° + x = 180°

x = 70°

Answer:

1) Null hypothesis:[tex]p \geq 0.4[/tex]  

Alternative hypothesis:[tex]p < 0.4[/tex]  

2) [tex]z=\frac{0.38 -0.4}{\sqrt{\frac{0.4(1-0.4)}{500}}}=-0.913[/tex]  

3) [tex]p_v =P(z<-0.913)=0.1806[/tex]  

4) For this case since the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly less than 0.4

a. Fail to reject the null hypothesis

Step-by-step explanation:

Information given

n=500 represent the random sample taken

[tex]\hat p=0.38[/tex] estimated proportion of if the people they are confident of meeting their goals  

[tex]p_o=0.4[/tex] is the value to test

represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Part 1

We want to test if the true proportion is less than 0.4, the system of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.4[/tex]  

Alternative hypothesis:[tex]p < 0.4[/tex]  

a. left-tailed

Part 2

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.38 -0.4}{\sqrt{\frac{0.4(1-0.4)}{500}}}=-0.913[/tex]  

Part 3

The p value for this case can be calculated like this:

[tex]p_v =P(z<-0.913)=0.1806[/tex]  

Part 4

For this case since the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly less than 0.4

a. Fail to reject the null hypothesis

Answer:

Answer:

-8 = x

Step-by-step explanation:

-15 = 2x + 1

-1            - 1            Subtract 1 from both sides

-16 = 2x                 Divide both sides by 2

-8 = x

To make sure this answer is correct, plug it into the equation to see if it works.

-15 = 2(-8) + 1       Multiply

-15 = -16 + 1          Add

-15 = -15

Answer:

See below.

Step-by-step explanation:

9.

Property of a rhombus:

In a rhombus, the diagonals are perpendicular.

The sum of the measures of the angles of a triangle is 180 deg.

Since the diagonals are perpendicular, the angles formed by the intersection of the diagonals are right angles and measure 90 deg.

m<ABD + m<CAB + 90 = 180

50 + m<CAB + 90 = 180

m<CAB + 140 = 180

(i) m<CAB = 40

The diagonals of a rhombus divide the rhombus into 4 congruent triangles.

Call the point of intersection of the diagonals E.

Triangles CEB and AEB are congruent.

m<BCA = m<DCA = 40

m<BCD = m<BCA + m<DCA = 40 + 40

(ii) m<BCD = 80

m<CDB = m<ADB = 50

m<ADC = m<CDB + m<ADB = 50 + 50

(iii) m<ADC = 100

10.

There are two angles labeled z. One is near point E and one is near point O. One of them probably is x.

Two angles measure 60 and 80. Add them to get 140.

z (near point O) and the 140 deg angle are a linear pair. their measures add to 180 deg.

z + 140 = 180

z = 40 (This is the z near point O.)

z (near point O) and 60 deg add to an interior angle of the parallelogram.

z + 60 = 40 + 60 = 100

The interior angle at vertex O measures 100 deg.

Adjacent interior angles of a parallelogram are supplementary.

100 + y = 180

y = 80

The two angles labeled z are alternate interior angles. Since the sides of a parallelogram are parallel, the two angles labeled z are congruent and measure 40 deg.

z = 40 (This is angle z near point E)

Answer:

  H  70 in³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = (1/3)Bh

  V = (1/3)(21 in²)(10 in) = 70 in³

The volume of the pyramid is 70 cubic inches.

Answer:

[tex]= 70 {in}^{3}[/tex]

Third answer is correct.

Step-by-step explanation:

[tex]v = \frac{base \: \: \: area \times height}{3} \\ = \frac{21 \times 10}{3} \\ = 70 {in}^{3} [/tex]

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Answer:

Jake

Step-by-step explanation:

Noah: 11 feet per second

Katie: 423 feet / 33 seconds = 12.82 ft/sec (just divide the feet / seconds)

Jake:

1 mile = 5280 feet

Adam runs 5280ft / 396 seconds = 13.34 ft/sec

Liz:

1 minute = 60 second.

Liz runs 638 feet / 60 seconds = 10.63 ft / sec

From the above results we find that Jake runs the fastest

Answer:

1) With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

2) The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

3) The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Step-by-step explanation:

The significance level for all the cases is the same [tex]\alpha=0.05[/tex]

Part 1

With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

Part 2

The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

Part 3

The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Answer:

12

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of line segment

[tex] = \frac{14 - 6}{10 - 8} \\ = \frac{8}{2} \\ =4[/tex]

Answer:

[tex]-3 \le h \le 1[/tex].

Step-by-step explanation:

Apply the property of absolute values: if [tex]a \ge 0[/tex], then [tex]|x| \le a \iff -a \le x \le a[/tex]. By this property, [tex]|- 3\, h - 6 | \le 3[/tex] is equivalent to [tex]-3 \le -3\, h - 6\le 3[/tex]. That's the same as saying that [tex]-3\, h - 6 \ge -3[/tex] and [tex]-3\, h - 6 \le 3[/tex].

Add [tex]6[/tex] to both sides of both inequalities:

[tex]-3\, h \ge 3[/tex] and [tex]-3\, h \le 9[/tex].

Divide both sides of both inequalities by [tex](-3)[/tex]. Note that because [tex]-3 < 0[/tex], dividing both sides of an equality by this number will flip the direction of the inequality sign.

Both inequalities are supposed to be true. Combining the two inequalities to obtain:

[tex]-3 \le h \le 1[/tex].

Answer:

Rhombus

Step-by-step explanation:

Answer:

Step-by-step explanation:

rhombus

Answer:

152°

Step-by-step explanation:

Let P be any point on tangent [tex] \overleftrightarrow{YZ} [/tex] and WY is secant or chord of the [tex] \odot J[/tex] .

[tex] \therefore m\angle WYZ + m\angle WYP = 180°\\(Straight \: line \: \angle 's) \\

\therefore 104° + m\angle WYP = 180°\\

\therefore m\angle WYP = 180°- 104° \\

\red{\boxed {\bold {\therefore m\angle WYP = 76°}}} \\[/tex]

NOW, by tangent secant theorem:

[tex] m\angle WYP =\frac{1}{2}\times m(\widehat{WXY}) \\\\

76°=\frac{1}{2}\times m( \widehat{WXY}) \\\\

76°\times 2 =m( \widehat{WXY}) \\

\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}} [/tex]

Step-by-step explanation:

work is shown and pictured

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

              = 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC = [tex]\frac{1}{2}(\widehat{AC}+\widehat{BD})[/tex]

143° = [tex]\frac{1}{2}[(x+5)+(x-5)][/tex]

143° = x

Therefore, Option (3) will be the answer.

Answer:

9 inches

Step-by-step explanation:

For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.

The width of the rectangle can be found as 9 inch.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The area and length of rectangle are given as 54 inch² and 6 inches.

Suppose the width of the rectangle be x.

Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,

6x = 54

⇒ x = 54/6

⇒ x = 9

Hence, the width is given as 9 inch.

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Answer:

Step-by-step explanation:

I remember leaving a top of ten percent (15%)

lets convert 15% into a decimal

15%=0.15

Tip=0.15x, where x is the bill price

Tip=0.15*34

Tip=5.1

So he could get  5$ and 10 cents as a tip

Simplify the expression.

[tex]\frac{y}{2} +\frac{40}{3}[/tex]

Answer:

Endangered species

Step-by-step explanation:

An endangered species is a species that is at risk of extinction due to rapid decrease in their population .Their decrease in population might be due to loss of habitat and genetic variation. The loss of habitat might be due to natural factors like the climate change For example animals like dinosaurs during the cretaceous period that experience rapid change in the climate loss their habitat and went extinct.

Human activity can also influence loss of habitat. Development in housing , agriculture and industry can also threaten the habitats of native organisms. The loss of their habitat might cause sudden extinction of these organisms. They might find it hard to adapt to another environment or even procreate.  

Generally,  endangered species are species that are threatened by extinction. Elephants that are in danger of been wiped out is an endangered species.

Answer:

A tangent line touches a curve at one point and has the same slope as the curve at that point. A secant line intersects at 2 or more points and has a slope equal to the average rate of change between those points.

Answer:

A Tangent of a circle is found outside of the circle but touching 2 points of the circle on the outside. But a Secant is found inside the circle and it touches 2 points in the circle. A Chord can always be Secant, but a secant can not always be a chord because it may pass through the circle.

Step-by-step explanation:

Answer:

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Step-by-step explanation:

Given a function y, the average rate of change S of y=f(x) in an interval [tex](x_{s}, x_{f})[/tex] will be given by the following equation:

[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}[/tex]

In this problem, we have that:

[tex]B(t) = 1000(1.02)^{t}[/tex]

Find the average rate of change in the balance over the interval t = 0 to t = 5.

[tex]B(0) = 1000(1.02)^{0} = 1000[/tex]

[tex]B(5) = 1000(1.02)^{5} = 1104.08[/tex]

Then

[tex]S = \frac{1104.08 - 1000}{5-0} = 20.82[/tex]

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Answer:

(0, 8).

Step-by-step explanation:

The y intercept occurs when  = 0, so we have the equation:

y = -3(0) + 8

y = 0 + 8

y = 8.

The answer is (0, 8).