What is the slope of the line passing through the points (7, 10) and (5, 16) ?
Thank you

Answer:

Step-by-step explanation:

f(x) is like y in a linear equation. There is one major difference. F(x) tells you what to substitute on the right every time you see an x.

f(a) = -3a + 7

f(b) = -3b + 7

For this question a and b have values. Now work with the right side only. This is the quickest way to get the answer, but it is only marginally correct.

f(a) = -3(-8) + 7 = 24 + 7 = 31

f(b) = -3(7) + 7 = -21 + 7 = - 14

f(a) + f(b) = 31 - 14 = 17

f(a) - f(b) = 31 - (-14) = 31 + 14 = 45

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

Learn more about confidence intervals;

https://brainly.com/question/24131141

#SPJ1

Answer:

Thanks

Step-by-step explanation:

Thanks

The second number in the ordered pair is the y coordinate.

The second value of an ordered pair is the y-value.

It signifies how far above (or below) the x axis o (horizontal axis) that a point is. If the y value is positive, then the point is above the x-axis, but if it is negative it is below the x axis (when it's 0, the point is on the x-axis)

**NOTE** the x and y axes are on the Cartesian plane

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

Learn more on zeros of a function here;

https://brainly.com/question/16550963

#SPJ1

Answer:

B) \(-\frac{a}{-b}\)

Step-by-step explanation:

The value \(-\frac{-a}{b}\) is the same as \(\frac{a}{b}\) since the negatives cancel out to make a positive.

Option A is incorrect since the overall value of the term would be negative. Option B however is correct since there will not be a negative value in the denominator of a fraction and thus it cancels out with the negative in front of the fraction to produce the value of \(\frac{a}{b}\) which is the same as the expression given in the question, thus it is option B.

The fraction which is equivalent to 0.5 is 1/2

So the answer is basically B

Answer:

1661.06 cm²

Step-by-step explanation:

From the question given above, the following data were obtained:

Radius (r) = 11.5 cm

Size of synthetic leather needed =?

To know how many square centimetres of synthetic leather needed to cover the ball, we shall determine the area of the ball. This can be obtained as follow:

Radius (r) = 11.5 cm

Pi (π) = 3.14

Area of ball =?

The shape of a ball is spherical in nature. Thus, we shall apply the formula for calculating the area of a sphere. This is illustrated below:

A = 4πr²

A = 4 × 3.14 × 11.5²

A = 4× 3.14 × 132.25

A = 1661.06 cm²

Thus, 1661.06 cm² of synthetic leather needed to cover the ball.

=========================================

Explanation:

Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.

So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below

We could also swap the order of either x, y or z, and still have the same result.

Answer:

14 burgers

Step-by-step explanation:

3 1/2 ÷ 1/4 = 14

Answer:

x= -28.173

Step-by-step explanation:

formula for quadratic equation, y= (-b±√(b²-4ac))/(2a)

a= 1, b= -4 and c= -1

y= 4 + √(16+4)

= 4 + √20

here,

sinx = y

sinx = 4+ √20

or, x= sin^-1 (4+√20)

which doesn't exist

taking

sinx = 4-√20

x = -28.173°

Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

https://brainly.com/question/22062407

#SPJ2

The slope of tangent to a curve is found by equating the derivative to the x - coordinate to y - coordinate of the tangent.

Tangent, in geometry, the tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point. It may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve as the second point approaches the first.

In Geometry, the tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.

In geometry, a tangent is the line drawn from an external point and passes through a point on the curve. One real-life example of a tangent is when you ride a bicycle, every point on the circumference of the wheel makes a tangent with the road.

Therefore,

The slope of tangent to a curve is found by equating the derivative to the x - coordinate to y - coordinate of the tangent.

To learn more about Slope visit :

brainly.com/question/9631381

#SPJ4

Answer:

between 14 and 15

Step-by-step explanation:

convert fractions using 42 as the LCD, then add:

59/7 = 354/42

37/6 = 259/42

354/42 + 259/2 = 613/42 = 14.6

14 < 14.6 < 15

or,

convert fractions to decimals, then add:

59/7 = 8.4

37/6 = 6.2

8.4 + 6.2 = 14.6

The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To know more about Confidence interval visit: https://brainly.com/question/29680703

Answer:

1.3a

Step-by-step explanation:

Option B) 17

A simple kind of data visualization known as a "dot plot" involves the representation of data points as dots on a graph with x and y axes. Sai has 17 albums in his collection altogether.

Given data;

6 = 0; 7 = 1 ; 8 = 2; 9 = 2; 10 = 4; 11 = 1; 12 = 2; 13 = 2; 14 = 1; 15 = 0; 16 = 2

\(= 1+2+2+4+1+2+2+1+2\)

\(=17\)

The total number of albums in Sai collection is 17

A basic style of data visualization called a dot plot, often referred to as a strip plot or dot chart, shows data points as dots on a graph with x and y axes. The purpose of these graphs is to visually portray particular data patterns or groups.

Each dot in the provided dot plot represents an album. As a result, the total number of dots in the dot plot equals the total number of albums in Sai's collection.

For such more question on Dot Plot:

brainly.com/question/22746300

#SPJ4

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

For more such questions on dedication, click on:

https://brainly.com/question/30160240

#SPJ8

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

For such more questions on amount

https://brainly.com/question/24644930

#SPJ8

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

The appropriate hypothesis test is a two-sample t-test for independent samples.

The appropriate hypothesis test in this scenario is a two-sample t-test for independent samples. Since the population standard deviations are known, we can use the Z-test instead.

The test statistic can be calculated using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

x1 and x2 are the sample means for Manufacturer A and Manufacturer B, respectively.

s1 and s2 are the population standard deviations for Manufacturer A and Manufacturer B, respectively.

n1 and n2 are the sample sizes for Manufacturer A and Manufacturer B, respectively.

Plugging in the given values:

x1 = 179, x2 = 178, s1 = 1, s2 = 5, n1 = n2 = 108

t = (179 - 178) / sqrt((1^2 / 108) + (5^2 / 108))

t = 1 / sqrt(0.00926 + 0.0463)

t ≈ 1 / sqrt(0.05556)

t ≈ 1 / 0.2357

t ≈ 4.241

To determine whether there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different, we compare the calculated t-value to the critical value from the t-distribution at the desired significance level (0.05).

The decision depends on the degrees of freedom for the test, which is calculated as (n1 + n2 - 2) = (108 + 108 - 2) = 214.

Using a t-table or statistical software, we find that the critical value for a two-tailed test with a significance level of 0.05 and 214 degrees of freedom is approximately ±1.972.

Since the calculated t-value of 4.241 exceeds the critical value of 1.972, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different at the 0.05 significance level.

For more such question on hypothesis

https://brainly.com/question/25263462

#SPJ8

Answer:

8:15:30

Step-by-step explanation:

8:15:30 a.m hope I helped ;)

Answer:

$15.21

Step-by-step explanation:

Answer:

15.21

Step-by-step explanation:

20−4.79

Subtract 4.79 from 20 to get 15.21.

15.21

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

Answer:option D for the first one

Step-by-step explanation:

It adds up to what they bought

Answer:

2

Step-by-step explanation:

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

For more questions on length of a pendulum

https://brainly.com/question/28385005

#SPJ4

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

To solve more questions on probability, visit the link below -

https://brainly.com/question/10498558

#SPJ1

Answer: Solve for P: WR - 1 =R (1 – P) 10. ... Solve for B: A= 2B + C 12. ... 9. Solve for P: WR - 1 =R (1 – P).

Step-by-step explanation: