3. What is the slope and y-intercept of the linear equation y = -7x + 5 ? (2 points)
slope = 1/7
y-intercept = (5,0)
slope = 7
y-intercept = (5,0)
slope = -1/7
y-intercept = (0,5)
slope = -7
y-intercept = (0,5)

By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.

Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.

Given,

The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.

Distance of 7th obstacle = x

Let,

Distance of 9th obstacle = y

Distance of 3rd obstacle = x'

Distance of 4th obstacle = y'

Distance between obstacle 3 and 7 = x - x'

Distance between obstacle 4 and 9 = y - y'

Distance between obstacle three and obstacle four = x' - y'

Distance between obstacle seven and obstacle nine.= x - y

According to the question

x-x' = y-y'

⇒ x - y = x' - y'

Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.

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Answer:

y=3 maybe

Step-by-step explanation:

Answer:

\(slope \: = - 2x \\ y - intercept \: = 0 \: or \: (0,0)\)

I inserted an image of the equation.

Step-by-step explanation:

Hope this helps!

Answer:

Slope = -2

Y-intercept = 0

Step-by-step explanation:

Hello!

Slope-Intercept Form: \(y = mx + b\)

Given our equation: \(y =-2x\)

Start at the origin, go down 2 units and to the right 1. Keep plotting points until you have enough to make a line.

Numerical variables can be subdivided into two types: discrete variables and continuous variables.

Discrete Variables: Discrete variables are numeric variables that take on a finite or countable number of distinct values. These values are typically whole numbers or integers. For example, the number of students in a classroom, the count of items in a store inventory, or the number of cars in a parking lot are all examples of discrete variables. Discrete variables cannot have values between the defined data points.

Continuous Variables: Continuous variables are numeric variables that can take on any value within a specified range or interval. They can be measured to a high degree of precision. Continuous variables are often obtained through measurements or observations and can have decimal values. Examples of continuous variables include height, weight, temperature, time, and distance. Continuous variables can have an infinite number of possible values within the given range.

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Answer:

y ≤5

Step-by-step explanation:

The range is the possible y values

The largest that y gets is 5

y ≤5

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Fallis has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

To find out if Ms. Fallis has enough tiles to cover the counter, we need to calculate how many tiles are required to cover an area of 2 square meters.

Since the tiles have a side length of 3 centimeters, we need to convert the area of the counter to square centimeters.

1 square meter = 10000 square centimeters (cm²)

So, 2 square meters = 20000 square centimeters (cm²)

Now, we need to calculate the area of each tile:

Side length of each tile = 3 centimeters (cm)

Area of each tile = \((side length)^2\) = \((3 cm)^2\) = 9 square centimeters (cm²)

To cover the counter, we need to divide the total area of the counter by the area of each tile:

Number of tiles required = (Total area of counter) / (Area of each tile)

= 20000 cm² / 9 cm²

= 2222.22

Since we cannot have a fraction of a tile, we need to round up to the nearest whole number of tiles. So, Ms. Fallis needs at least 2223 tiles to cover the counter.

Since she has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

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The Marginal Rate of Substitution (MRS) for the given function is equal to -2/sqrt(x). To find the Marginal Rate of Substitution (MRS), we need to take the derivative of the given function with respect to x.

Given: y = 24 - 4(sqrt(x))

Step 1: Differentiate the function y with respect to x.

dy/dx = d/dx(24 - 4(sqrt(x)))

Step 2: Differentiate each term separately using the power rule and chain rule.

dy/dx = 0 - 4(1/2)(x^(-1/2))(1)

Step 3: Simplify the derivative.

dy/dx = -2(x^(-1/2))

Step 4: Rewrite the derivative in terms of MRS.

MRS = dy/dx = -2/sqrt(x)

Therefore, the Marginal Rate of Substitution (MRS) for the given function y = 24 - 4(sqrt(x)) is -2/sqrt(x).

The negative sign indicates that the MRS is inversely related to x, which means as x increases, the MRS decreases. The value of MRS represents the rate at which a consumer is willing to substitute y (the dependent variable) for an incremental change in x (the independent variable). In this case, as x increases, the consumer is willing to substitute less y for the additional units of x.

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Answer:

Step-by-step explanation:

y = m(x-x_1)+y_1

y = -2(x-(-3))+4

y = -2(x+3)+4

y = -2x-6+4

y = -2x-2

-Hope this helps!

The proportion of defective corks produced by this machine through z test comes out is 0.320.

Given mean of 2 cm and standard deviation of 0.1 cm, The diameter is between 1.9 and 2.1 cm.

We have to find the proportion of defective corks that are produced by machine.

In this problem we have to first find z score and then we will be able to find the probability of defective corks produced by the machine.

Z=(X-μ)/σ

μ=2 cm and σ=0.1 cm.

Z value corresponding to X=1.9.

Z=(1.9-2)/0.1

=-0.1/0.1

=-1

Z value corresponding to X=2.1.

Z=(2.1-2)/0.1

=0.1/0.1

=1

P value of P(-1<Z<1)=2*0.3410=0.6820

Proportion of corks which are not defective=0.6820.

Proportion of corks which are defective=1-0.680.

=0.320

Hence the proportion of defective corks produced by machine is 0.320.

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Profit fall in one year = 116.8$

What is profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are several profit metrics that are frequently used.

Let cost price = C

And selling price before reducing = S

Profit for 1 day = S-C

Now, After reducing selling price to = S-0.32

Profit= S - 0.32 - C for 1 day

Profit fall by = (S-C)-(S - 0.32 - C)

                     = S - C - S + 0.32 + C

Profit fall by = 0.32 for 1 day

Profit fall by one year = 0.32×365

                                    = 116.8$

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Rounding to three decimal places, the critical value is ±2.109.

The critical value for a 95% confidence interval, we need to look up the t-distribution with degrees of freedom given by:

df = [(s1²/n1 + s2²/n2)²] / [((s1²/n1)²/(n1-1)) + ((s2²/n2)²/(n2-1))]

s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.

Plugging in the values given in the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

Using a t-distribution table or a calculator, we can find the critical value for a 95% confidence interval with 17 degrees of freedom:

\(t_c\) = ±2.109We must get the crucial value for a 95% confidence interval using the degrees of freedom provided by the following t-distribution:

(S12/n1 + S22/n2)2 = df ((s22/n2)2/(n2-1)) + ((s12/n1)2/(n1-1))))

The sample standard deviations are s1 and s2, and the sample sizes are n1 and n2.

Inserting the values from the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

We may get the crucial value for a 95% confidence interval with 17 degrees of freedom using a t-distribution table or a calculator:

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Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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To determine if there is a difference between the bacterial samples collected from the bottom of your shoes and the door handle to the bathroom, you would use a statistical method called hypothesis testing.

Hypothesis testing allows us to make inferences about a population based on a sample of data. In this case, you have two samples (bottom of shoes and door handle) and want to determine if there is a significant difference between the two in terms of bacterial colonies.

The specific hypothesis test to use would depend on the nature of the data and the distribution assumptions. One commonly used test is the independent samples t-test, which compares the means of two independent samples to assess if there is a statistically significant difference between them.

In this scenario, you would collect data on the number of bacterial colonies from each sample, and then perform an independent samples t-test to analyze the data. The test would provide a p-value, which indicates the probability of observing the difference in bacterial colonies between the two samples if there were no true difference in the population. Based on the p-value, you can make a decision regarding the presence or absence of a significant difference between the samples.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 4

gives the next term. In other words,

an=a1.rn-1.

Geometric Sequence:

R=4

This is the form of a geometric sequence.

an=a1rn-1

Substitute in the values of

a1=11 and

r=4.an=(11)(.)4)n-1

Remove parentheses.

an=11.4n-1

Answer:

11,-88,704

Step-by-step explanation:

what exactly do u mean

(a) To find the maximum rate of change of f at point P(1,0), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.

The gradient of f is:

∇f(x,y) = <y cos(xy), x cos(xy)>

At point P(1,0), we have:

∇f(1,0) = <0, cos(0)> = <0, 1>

The magnitude of the gradient is:

||∇f(1,0)|| = \(sqrt(0^2 + 1^2)\) = 1

Therefore, the maximum rate of change of f at point P is 1, and it occurs in the direction of the unit vector in the direction of the gradient:

u = <0, 1>/1 = <0, 1>

So the maximum rate of change occurs in the y-direction.

(b) To find the maximum rate of change of f at point P(8,1.3), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.

The gradient of f is:

∇f(x,y,z) = <2x, 2y, 2z>

At point P(8,1.3), we have:

∇f(8,1.3) = <16, 2.6, 2(1.3)> = <16, 2.6, 2.6>

The magnitude of the gradient is:

||∇f(8,1.3)|| = \(sqrt(16^2 + 2.6^2 + 2.6^2) = sqrt(275.56) ≈ 16.6\)

Therefore, the maximum rate of change of f at point P is approximately 16.6, and it occurs in the direction of the unit vector in the direction of the gradient:

u = <16, 2.6, 2.6>/16.6 ≈ <0.963, 0.157, 0.157>

So the maximum rate of change occurs in the direction of this unit vector.

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The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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Answer:

I think it is 30

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The angles shown are vertical angles

If you didn't know vertical angles are congruent

That being said we create an equation to solve for x

(because vertical angles are congruent) 104 = 3x + 14

now that we have created an equation we want to solve for x

Step 1 subtract 14 from each side

104 - 14 = 90

14 - 14 cancels out

now we have 90 = 3x

step 2 divide each side by 3

90/3=30

3x/3=x

we're left with x = 30

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The probability that the balls are both white be 1/7.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Number of black balls = 4

Number of white balls = 3

Total number of balls = 7

Number of ways of picking up a white ball out of 7 balls, P(W) = 3/7

Number of ways of picking up a second white ball ,P(W) = 2/6

Therefore, the probability of picking up 2 white balls

P(WW) = 3/7 \(*\) 2/6 = 1/7

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Answer:

5:7

Step-by-step explanation:

Answer:

First that's a  quiz. Lol

Step-by-step explanation:

It is the 2'nd answer.

Your Welcome.

The probability of randomly choosing a number either divisible by 5 or divisible by 3 is 1/2.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of randomly choosing a number either divisible by 5 or divisible by 3 = (numbers divisible by 3 / total number) + (numbers divisible by 5 / total number)

10/32 + 6/32 = 16/32=  1/2

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Answer:

7/16

Step-by-step explanation:

Answer: W = 6.3

w ÷ 9 = 0.7

1. We need to convert the non-repeating decimal (0.7) into a rational number. We can rewrite the given number as a fraction, where the numerator is equal to the number after then decimal point, and the denominator is equal to \(10^n\), when n is the number of decimal places. In the problem, n equals 1.

w ÷ 9 = \(\frac{7}{10}\)

2. Now, we'll need to factor the integer, which is 9. To do that, repeatedly divide it by the ascending sequence of primes (2, 3, 5...). The number of times that each prime divides the original integer becomes its exponent in the final result. In the problem, 3 to the 2nd power is 9.

3 x 3 = 9

w ÷ 9 = \(\frac{7}{10}\) ⇒ \(\frac{w}{3^2}=\frac{7}{2\times5}\)

Hence, W = 63/10, but we aren't done. We'll need to divide 63 by 10.

63 ÷ 10 = 6.3

Our final answer is 6.3

Let me know if you have any questions.

~ Lily, from Brainly.

To the nearest cent, the amount she would have in 2 years is $44.10

What is future value of the deposit in savings account?

The future value of the savings account deposit is accumulated balance in the account after 2 years which includes the initial deposit plus interest earned over 2 years

FV=PV*(1+r)^N

FV=accumulated balance after 2 years=unknown

PV=initial deposit=$40

r=interest rate per year=5%

N=number of years that the deposit would last=2

FV=$40*(1+5%)^2

FV=$44.10

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The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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The completed table that proves the congruence of the triangles are presented as follows;

Statement \({}\)                                                 Reasons

1. ∠BAC ≅ ∠EDC  \({}\)                                   1. Given

\(\overline{BC}\) ≅ \(\overline{EC}\)              \({}\)                              

2. ∠ACB ≅ ∠DCE     \({}\)                               2. Vertical angles theorem

3. ∠ABC ≅ ∠DEC \({}\)              \({}\)           \({}\)          3. Angle sum property of triangle

4. ΔABC ≅ ΔDEC \({}\)                                   4. ASA congruence rule

8. Statement \({}\)                                          Reasons

1. \(\overline{JK}\) ≅ \(\overline{LM}\)                                             1. Given

2. ∠JKM ≅ ∠LMK \({}\)                                   2. Given

3. \(\overline{MK}\) ≅ \(\overline{KM}\)    \({}\)                                     3. Reflexive property

4. ΔJMK ≅ ΔLKM \({}\)                                   4. SAS congruence rule

Triangles are congruent if they have the same size and shape.

The details of the reasons used to prove the congruence of the triangles are as follows;

Vertical angles theorem;

The vertical angles theorem states that the vertically opposite angles formed by two intersecting straight lines are always congruent.

Angle sum property of a triangle

The angle sum property of a triangle states that the sum of angles in a triangle is 180°.

Therefore, if two angles are known in a triangle, the third angle can be calculated as the difference between 180° and the sum of the two known angles.

ASA congruence rule

The ASA (which is an acronym for Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Reflexive property of congruence

The reflexive property states that a segment is congruent to itself

SAS congruence rule

The SAS (Side-Angle-Side) congruence rule states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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