Jennifer is saving money to buy a bike. The bike costs $223. She has "$128" saved, and each week she adds $19 to her savings.

Check the picture below.

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

3/5 x less then or equal to sign 21

Step-by-step explanation:

just trust me

The daughter's age​ is 2 years.

If an equation is written in the form ax + by + c = 0 and the coefficients of x and y, i.e., a and b are not equal to zero, then it is said to be a linear equation in two variables.

Let the daughters age be x and woman age be y,

Forming the linear equations,

Woman is 4 times as old as her daughter, so

y = 4x

After five years, the Square of her age will exceed the Square of her daughter's age by 120 years, so

\((y+5)^2=(x+5)^2+120\)

Now, putting the value of y in second equation and finding the value of x,

\((4x+5)^2=(x+5)^2+120\\\\16x^2+25+40x=x^2+10x+25+120\\15x^2+30x-120=0\)

Solving the equation for x,

\(x^2+2x-8=0\\x^2+4x-2x-8=0\\x(x+4)-2(x+4)=0\\(x+4)(x-2)=0\\x=2\)

x=-4 is neglected because age can never be negative, so the daughter's age​ is 2 years.

Therefore, the age of daughter is 2 years.

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Answer:

B) There is convincing statistical evidence to suggest that political affiliation and where a person lives are dependent.

Step-by-step explanation:

Chi square test value is greater than the p-value which suggest that we can reject the null hypothesis and there is strong evidence supporting the statement of alternative hypothesis.

The conclusions, made for political affiliation, that there is convincing statistical evidence to suggest that political affiliation and where a person lives are dependent.

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

The analyst took a random sample of 1,250 people in a state. The following are the hypotheses the analyst tested-

The chi-square test statistic and p-value of the hypothesis test were 19.78 and 0.003 respectively.

The value of chi square is greater than p-value as,

\(19.78 > 0.003\)

Therefore, the null hypothesis can be rejected. There is an association between party affiliation and the county in which a person lives.

Hence, the conclusions, made for political affiliation, that there are convincing statistical evidence to suggest that political affiliation and where a person lives are dependent.

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A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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Answer:

take 1/2 multiply by sin 91°×2×8

Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.

Answer:B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

               3x = -6 --->  x = -2

Answer:

your answer is correct

Step-by-step explanation:

7(2) = 14

7(4) = 28

To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

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The algebraic expression for Desmond's height is x + 5.

If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.

So the algebraic expression for Desmond's height is x + 5.

Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).

They can contain one or more variables and can be evaluated for different values of the variables.

For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.

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When three college students are randomly selected, the probability that ALL three buy their textbooks online is 0.227

The probability that at least one purchases their textbooks online is 1.

As per the question the probability of students purchase their textbooks online 61%.

\(=\frac{61}{100}\)

p = 0.61.

So, failure = 1 - 0.61 = 0.39

q = 0.39

When 3 students are selected(n = 3)

We know that, \($$p(x)={ }^n c_x p^x q^{n-x}$$\)

So, probability that all of them to purchase

\($$\begin{aligned}&(x=3) \\& p(3)={ }^3 c_3(0.61)^3(0.39)^{3-3} \\& p(3)=0.22698\end{aligned}$$\)

When 5 students are selected (n = 5)

And probability that at least one purchases books online

\(=P(x=1)+P(x=2)+P(x=3)$ $+P(x=4)+P(x=5)$\)

Now we know that probability of all equal to 1.

\(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1\)

So, we can simply write

\($$\begin{aligned}P & =1-p(x=0)+p(x=1) \\& =1-\left[{ }^5 C_0(0.61)(0.35)^{50}+{ }^5 C_1(0.61)^1(0.39)^{5-1}\right] \\& =1-0.00902-0.07056 \\P& =0.92042\end{aligned}$$\)

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The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

The circumference of a circle with diameter 6cm is 18.85 cm.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that diameter of a circle is 6 cm.

We need to find the circumference  of circle with diameter 6 cm.

The formula to find circumference of circle=2πr

Radius=Diameter/2

=6/2=3 cm

Circumference of circle=2×3.14×3

=18.85

Hence, the circumference of a circle with diameter 6cm is 18.85 cm.

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Answer:

Step-by-step explanation:

18.8

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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Thus, the value of x and y for the given angle of  cyclic quadrilateral are found as y = 65 and x = 97.

A four-sided object with a circle-inscribed perimeter is referred to as a cyclic quadrilateral. The quadrilateral's four chords connect each of its four vertex points, which are located on the circle's equator. A cyclic quadrilateral has opposite angles that measure a total of 180 degrees.

Given that:

∠C =  120°

∠ D = 80°

∠A = y - 5

∠B = x + 3

Using the property of cyclic quadrilateral:

opposite angles add up to 180°

∠A + ∠C = 180

y - 5 + 120  = 180

y - 5 = 60

y = 65

Now,

∠B + ∠D = 180

x + 3 + 80  = 180

x + 3 = 100

x = 97

Thus, the value of x and y for the given angle of  cyclic quadrilateral are found as y = 65 and x = 97.

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Answer:

Adding +6 in turn

Step-by-step explanation:

-13+6=(-7)

(-7)+6=(-1)

(-1)+6=5

5+6=11

11+6=17

17+6=23

23+6=29

29+6=35

........... And so on

Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer:

t<=66

Step-by-step explanation:

at least 11 laps means greater than or equal to 11 laps.laps =l

It says Alan runs each lap in 6 minutes.

t<= 6l where l are the number of laps .

t<=66

Answer:

t<66

Step-by-step explanation:

1 lap=6 min

11×6=66 min

t<66

Answer:

Step-by-step explanation:

4 - 2x - 8x > -6x - 16

4 - 10x > -6x - 16

4 - 4x > -16

-4x > -20

x < 5

If a research institute poll asked respondents if they felt vulnerable to identity theft:

a) Population proportion p

Using this formula to find the  population proportion p.

p = (x/n)

Let plug in the formula

p = 584/1024

p= 0.57

b) Margin of error

Value of z-score for a confidence level of 95%= 1.96

Using this formula to margin of error

MOE =( z alpha x √(p) (1-p) / n )

Let plug in the formula

MOE =( 1.96 x √(.57)(1-.57) / 1024)

MOE =( 1.96 x √(.57)(.43) / 1024)

MOE =( 1.96 x √0.000239

MOE =( 1.96 x 0.015459)

MOE = 0.030

c) Confidence interval

Confidence interval =0.57 ± 0.030

Confidence interval = (0.57 -0.030) , (0.57 +0.030)

Confidence interval = 0.54; 0.6

Confidence interval = 0.54 <p< 0.6

d) The  statement that correctly interprets the confidence interval is:

a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Therefore the Population proportion p is 0.57, MOE is 0.030 and CI is  0.54; 0.6.

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The complete question is:
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=1024 and x=584 who said "yes"  Use a 95% confidence level.

a) Find the best point estimate of the population proportion p.

b) Identify the value of the margin of error E.

c) Construct the confidence interval.

d) Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow

a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

b) 95% of sample proportions will fall between the lower bound and the upper bound.

c) there is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

d) One has 95% confidence that the sample proportion is equal to the population proportion

The given statement "horizontal and vertical lines draw out notice because they appear more visually active than diagonal lines." is false.

In geometry, the term line is referred as the path of a moving point through space.

Here we have given the statement "horizontal and vertical lines draw out notice because they appear more visually active than diagonal lines."

And we need to identify whether the given statement is true or not.

While we looking into the given problem, we know that the diagonal line in a composition is considered to be the most dynamic line and suggests movement along that path and they are straight lines that slant in any direction except horizontal or vertical.

Based on this definition, we have identified that the given statement is false.

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Answer:

my best guess would be use a calculater

Step-by-step explanation:

Answer:

The first one is 6

The second one is 15

the third one is 5

the last one is 200

Step-by-step explanation:

Answer:

\(h \geq 2\)

Step-by-step explanation:

h has to be 2 or more since there is at least 2 hours.

Consider the given radical,

Factorize the number,

Consider the following properties,

Then the radical can be simplified as,

Thus, the radical is simplified as,