Determine which ratio forms a proportion with start fraction 14 over 35 end fraction by writing the ratio in simplest form.
A. start fraction 2 over 7 end fraction
B. four-fifths
C. three-eighths
D. two-fifths

Answer: A) y= -1/2x+5

Step-by-step explanation: If the line is perpendicular to the original, the  new "m" (coefficient  of x) has to be the negative reciprocal of the original "m"

= 0.0655.

This is stated in a different way and i would take this as 3 non defective before first defective on the 6th inspection. That would be 0.8^3*0.2 = 0.0655.

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Answer:

9.5

Step-by-step explanation:

Answer:

  a) multiply by cos²/cos², move sin/cos inside parentheses, simplify

  d) multiply by (cot+cos); use cot=cos·csc, csc²-1=cot² in the denominator

Step-by-step explanation:

You want to prove the identities ...

Usually, we want to prove a trig identity by providing the steps that transforms one side of the identity to the expression on the other side. Here, each of these identity expressions can be simplified, so it is actually much easier to simplify both expressions to one that is common.

We are going to use s=sin(x), c=cos(x), (s/c) = tan(x), and (c/s) = cot(x) to reduce the amount of writing we have to do.

  \(s^2\left(\dfrac{c}{s}+1\right)^2=c^2\left(\dfrac{s}{c}+1\right)^2\qquad\text{given}\\\\\\\dfrac{s^2(c+s)^2}{s^2}=\dfrac{c^2(s+c)^2}{c^2}\qquad\text{use common denominator}\\\\\\(c+s)^2=(c+s)^2\qquad\text{cancel common factors; Q.E.D.}\)

Using the same substitutions as above, we have ...

  \(\dfrac{c(c/s)}{(c/s)-c}=\dfrac{(c/s)+c}{c(c/s)}\qquad\text{given}\\\\\\\dfrac{c^2}{c(1-s)}=\dfrac{c(1+s)}{c^2}\qquad\text{multiply num, den by s}\\\\\\\dfrac{c(1+s)}{(1-s)(1+s)}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{1-s^2}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{c^2}=\dfrac{c(1+s)}{c^2}\qquad\text{Q.E.D.}\)

__

Additional comment

The key transformation in (d) is multiplying numerator and denominator by (1+sin(x)). You can probably prove the identity just by doing that on the left side, then rearranging the result to make it look like the right side.

For (a), the key transformation seems to be multiplying by cos²(x)/cos²(x) and rearranging.

Sometimes it seems to take several tries before the simplest method of getting from here to there becomes apparent. The transformations described in the top "Answer" section may be simpler than those shown in the "Step-by-step" section.

The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

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In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

The load from the structural element is transferred to the foundation at a bearing point, which is often a concentrated load point.

To avoid structural failure, settling, or excessive deflection of the part, it is crucial to make sure the bearing point is properly designed and supported.

Since the bearing of C from A is 050°, we can find the bearing of A from C by adding 180° to 50°, which gives us:

Bearing of A from C = 50° + 180° = 230°

Therefore, In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

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Complete question -

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.

If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.

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In order to calculate the distance traveled on the Westley heading, we can use the Pythagorean Theorem, where the distance of 28 km is the hypotenuse of the right triangle:

So we have:

Therefore the ship traveled 12.2 km on the Westley heading.

Answer: 20,532

Step-by-step explanation:

17,400(.02)=348

348(9)=3132

17,400+3132=20,532

Answer:

Step-by-step explanation:

This is an exponential growth function of the form:

\(y=ab^x\) where a is the initial population and b is the growth rate. This could also be written as

\(y=a(1+r)^x\) which is a bit more accurate. We'll use that one. r is the percent growth: 2% for us.

Filling in the formula:

\(y=17400(1+.02)^x\) and then simplifying:

\(y=17400(1.02)^x\)

That's the model for this population. Filling in any number of years for x will give you the population y. Our time is 9 years:

\(y=17400(1.02)^9\)

Take care of the exponents first, giving us:

\(y=17400(1.195092569)\) and then multiply to get

y = 20,794.6 or 20,794 people (since you can't have 6/10 of a person)

Mia will pay a total of $4.5 for the shipping and handling of the t-shirt

From the question, we have the following parameters that can be used in our computation:

Cost of the shirt = $15

shipping and handling = 30%

The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation

Amount paid = original price * + shipping and handling

Substitute the known values in the above equation, so, we have the following representation

Amount paid = 15 * 30%

Evaluate the products

Amount paid = 4.5

Hence, the amount paid is $4.5

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Answer:

n=2.56

Step-by-step explanation:

y < -2x - 1

Or it could be some variation of this, like 2x + y < -1

If r is a nonzero rational number, then r is a product of two irrational numbers.

If q≠0 is rational and y is irrational, then qy is irrational.

: You know that if G

is a group and H≠G

is one of its subgroups then h∈H

and y∈G∖H

implies that hy∈G∖H

Proof: suppose hy∈H

You know that h−1∈H, and therefore y=h−1(hy)∈H

Contradiction

In our case, we have the group (R∗,⋅) and its proper subgroup (Q∗,⋅). By the arguments above q∈Q∗ and y∈R∖Q implies qy∈R∖Q

.

Simply multiply it by the square root of two to obtain an irrational number. A product of two irrational numbers, your original number is obtained by multiplying this irrational number by the square root of two, which is itself irrational.

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a) The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

b) the sum of squares: SSE = (11.3 - μA)² + (11.3 - μA)²

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

(a) To calculate the 95% confidence interval for τA - τB, we can use the formula:

CI = (τA - τB) ± t(α/2, df) * SE(τA - τB)

where t(α/2, df) is the t-score for the desired confidence level and degrees of freedom, and SE(τA - τB) is the standard error of the difference in means.

The degrees of freedom for the test can be calculated using the formula:

df = ∑(ni - 1)

Given the data:

nA = 12, nB = 8, and mean responses: μA = 11.3, μB = 8.4, μC = 10.2

We can calculate the standard error using the formula:

SE(τA - τB) = √((s²/nA) + (s²/nB))

where s² is the sample variance.

Calculating the degrees of freedom:

df = (nA - 1) + (nB - 1) = 11 + 7 = 18

Plugging in the values, we have:

SE(τA - τB) = √((4.9/12) + (4.9/8)) ≈ 1.313

The t-score for a 95% confidence interval with 18 degrees of freedom can be found using a t-table or statistical software. Let's assume the t-score is t*.

The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

You would need to consult a t-table or use statistical software to find the t* value. The interval would be calculated by substituting the appropriate values.

(b) To calculate the F-test statistic for the hypothesis τA = τB = τC, we can use the formula:

F = (MSA / MSE)

where MSA is the mean square due to treatments and MSE is the mean square error.

The mean square due to treatments can be calculated as:

MSA = SSA / (k - 1)

where SSA is the sum of squares due to treatments and k is the number of groups (in this case, k = 3).

The mean square error can be calculated as:

MSE = SSE / (N - k)

where SSE is the sum of squares error and N is the total sample size.

To calculate the sum of squares:

SSA = ∑(ni * (μi - μ)²)

SSE = ∑∑((yij - μi)²)

Given the data, we can calculate the sum of squares:

SSA = (12 * (11.3 - ((11.3 + 8.4 + 10.2) / 3))^2) + (8 * (8.4 - ((11.3 + 8.4 + 10.2) / 3))²) + (16 * (10.2 - ((11.3 + 8.4 + 10.2) / 3))²)

SSE = (11.3 - μA)² + (11.3 - μA)²

Hence, a) The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

b) the sum of squares: SSE = (11.3 - μA)² + (11.3 - μA)²

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True. Parametric tests are a category of statistical tests that can only be applied to data that meets certain criteria.

They make use of normal distribution assumptions when analyzing data, which means that a significant proportion of the data must follow a normal distribution for the test to produce valid outcomes

.A sample is a subset of the population that is being examined. The size of the sample has an impact on the accuracy of the study. If the sample size is insufficient, it may not be representative of the entire population. In small sample sizes, the main assumptions of parametric tests may be violated, and the results of the test may be skewed.

A sample is a group of individuals or objects from a population that are chosen for a study. The size of the sample is critical since it has a direct impact on the statistical accuracy of the data. A small sample size can cause the primary assumptions of parametric tests to be broken.

Parametric tests are a type of statistical test that can only be used with specific kinds of data. When parametric tests are used to evaluate data, it is assumed that the data follows a normal distribution. In general, this means that the data should be symmetric around the mean, with the majority of the data values being near the mean and fewer outliers. However, when the sample size is small, the accuracy of these assumptions may be in doubt.

As a result, it's crucial to ensure that you choose the proper statistical test based on the size of your sample and the distribution of your data.

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Answer:

Step-by-step explanation:

3 1/2 = 7/2 improper fraction

7 4/5 = 39/5  improper fraction

Answer:

3 1/2 = 7/2      7 4/5 = 39/5

Step-by-step explanation:

3 1/2, take the whole number and multiply by the denominator; 3 * 2 = 6, and then add 1. 6 + 1 = 7. 7/2

7 4/5, take the whole number and multiply by the denominator; 7 * 5 = 35, and add 4. 35 + 4 = 39. 39/5

We have the supplied Expressions (b - c) – 7 based on the Statement.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more mathematical functions. This mathematical main requirement the multiple, division, adding, or subtraction of numbers. The following is the architecture of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

According to it ,The phrase for the specified order.

= (b - c)

Next, take 7 out of the outcome. Consequently, the sequence's expression is

Consequently, the necessary phrase is (b - c) - 7.

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The student knows the answer to approximately 5 questions out of the 20.

Let's denote the event that the student knows the answer to a question as K and the event that the student answers the question correctly as C. We are given the following information:

P(K) = n/20 (probability that the student knows the answer)

P(C|K) = 1 (probability of answering correctly given that the student knows the answer)

P(K|C) = 0.824 (conditional probability that the student knows the answer given that the student answered correctly)

We can use Bayes' theorem to find the value of n:

P(K|C) = P(C|K) * P(K) / P(C)

P(C) = P(C|K) * P(K) + P(C|not K) * P(not K)

    = 1 * (n/20) + (1/2) * ((20-n)/20)

    = n/20 + (20-n)/40

    = (2n + 20 - n) / 40

    = (n + 20) / 40

Now, substituting the values into Bayes' theorem:

0.824 = 1 * (n/20) / ((n + 20) / 40)

0.824 = (2n / 20) * (40 / (n + 20))

0.824 = 4n / (n + 20)

Cross-multiplying:

0.824 * (n + 20) = 4n

0.824n + 16.48 = 4n

3.176n = 16.48

n = 16.48 / 3.176

n ≈ 5.18

Therefore, the student knows the answer to approximately 5 questions out of the 20.

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Answer:

469.4ft²

Step-by-step explanation:

We have ∆ WXY in the above question,

From which we have obtained the following values

Angle W = 27°

Angle X = ?

Angle Y = 40°

Side w =?

Side x = ?

Side y = 38ft

Area of the triangle= ?

Step 1

We find Angle X

We know that the Sum of angles in a triangle = 180°

In the question above, we are given 2 angles

Hence,

Angle X = 180 - ( Angle W + Angle Y)

= 180° - (27 + 40)°

= 180° - 67°

Angle X = 113°

Step 2

Find the sides w and x

We find these sides using the Rule of sines

Rule of Sines =

a/ sin A = b/ Sin B = c/Sin C

Hence for triangle WXY

w/ sin W = x/ sin X = y/ sin Y

We have the following values

Angle W = 27°

Angle X = 113°

Angle Y = 40°

We are given side y = 38ft

Determining side w

w/ sin W= y/ sin Y

w/sin 27 = 38/sin 40

Cross Multiply

sin 27 × 38 = w × sin 40

w = sin 27 × 38/sin 40

w = 26.83879ft

w = 26.84ft

Determining side x

w/ sin W = x/ sin X

26.84/ sin 27 = x/sin 113

Cross Multiply

sin 113 × 26.84 = x × sin 27

x = sin 113 × 26.84/sin 27

x = 54.42041ft

x = 54.42ft

To find the area of triangle WXY

We apply the use of heron formula

= √s(s - w) (s - x) (s - y)

Where S = w + x + y/ 2

s = (38 + 26.84 + 54.42)/2

s = 59.63

Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)

Area of the triangle = √ 220343.61423

Area of the triangle = 469.40772706541ft²

Hence, Approximately to the nearest tenth =469.4yd²

To find the measure of angle BCD, we need to determine the measure of angle BCA first.

In a regular 20-gon, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a 20-gon, the sum of the interior angles is (20-2) * 180 = 3240 degrees.

Since the 20-gon is regular, each interior angle has the same measure. Therefore, each interior angle of the 20-gon measures 3240 degrees / 20 = 162 degrees.

Angle BCA is one of the interior angles of the 20-gon, so it measures 162 degrees.

Now, in the heptagon BACD, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a heptagon, the sum of the interior angles is (7-2) * 180 = 900 degrees.

Since the heptagon is regular, each interior angle has the same measure. Therefore, each interior angle of the heptagon measures 900 degrees / 7 = 128.571 degrees (rounded to three decimal places).

Angle BCA is one of the interior angles of the heptagon, so it measures 128.571 degrees.

Finally, angle BCD is the difference between angles BCA and BCD: angle BCD = angle BCA - angle BCD = 162 degrees - 128.571 degrees = 33.429 degrees (rounded to three decimal places).

Therefore, angle BCD measures approximately 33.429 degrees.

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Let B, A, and D be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on \(ABbar\), with a vertex C next to A. Find\(\leqBCD\) ∠\(BCD\) , in degrees.

To determine the degrees of angle BCD in this problem, we must first discover the degree of each interior angle of the 20-gon and the heptagon. Calculating these values, and subtracting them from 180, we find the measure of angle BCD equals to 69.43 degrees.

In this problem, we need to find the measure of angle BCD of a heptagon formed on a side of a regular 20-gon. We have that consecutive vertices B, A, D of 20-gon and vertex C of a heptagon formed on line segment AB is our interest point.

Since A, B, D are consecutive vertices of a regular 20-gon, we first calculate the value of each interior angle using the formula (n-2)×180/n, where n is the number of sides. So the measure of each interior angle of the 20-gon is (20-2)×180/20 = 162 degrees.

The heptagon shares one of its vertices with the 20-gon (i.e., point A). Point C is a neighboring vertex of A in this heptagon. The angles of a regular heptagon are calculated in the same way, using the formula (7-2)×180/7, which gives approximately 128.57 degrees.

Therefore, to calculate the measure of angle BCD, let's note that it equals to (180 - angle BAC) + (180 - angle CAD). Since angles BAC and CAD are parts of the 20-gon and the heptagon respectively, it will be (180 - 162) + (180 - 128.57) = 18 + 51.43 = 69.43 degrees.

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The correct unit price is $1.24 per pair of padded gloves such that the contractor's unit price is incorrect because total cost was divided by number of dozens bought instead of the number of units in 6 dozens

How many units are in a dozen?

The dozen of pairs of padded  gloves contains 6 pairs of padded  gloves, in other words, the number of units in 6 dozens is 6 dozens multiplied by 12 units in a dozen

number of units in 6 dozens=6*12

number of units in 6 dozens=72

unit price=total cost/number of units in 6 dozens

unit price=$89.28/72

unit price=$1.24

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Answer:

true

Step-by-step explanation:

true

the answer is true mommy

Answer:

5 cars

Step-by-step explanation:

If the average of cost of a car is $4,000 there will be enough cash to buy 5 cars. 20,000 divided by 4,000= 5.

Answer:

2,750

Step-by-step explanation:

Answer:

2,750

Step-by-step explanation:

9% of 25,000= 2,250

2,250+500=2,750

You are buying bottles of a sports drink for a softball team. Each bottle costs 1.19  Then the  total cost of purchasing 15 bottles of the sports drink is $17.85.

The function rule that models the total cost of a purchase is given by:

Total cost = Cost per bottle × Number of bottles

In this case, the cost per bottle is $1.19, and the number of bottles is the variable, which we can denote as "x." Therefore, the function rule can be written as:

Total cost = 1.19x

To evaluate the function for 15 bottles, we substitute the value of 15 for "x" in the function:

Total cost = 1.19 × 15

Total cost = $17.85

Therefore, the total cost of purchasing 15 bottles of the sports drink is $17.85.

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Answer:

$10 owed for lunch.

Step-by-step explanation:

"asset" means to benefit, so the question is asking which one of these is not benefiting his net worth. he has $15 and $25 in savings, these both benefit him. he also has a $50 rare baseball card this also benefits him. the only one that takes away money is the money he owes for lunch.

Consumption of Bananas per year = 5, 250, 000 metric tons

We know 1000 kg = 1 metric ton, so

Consumption of Bananas per year (in kg) = 5, 250, 000 x 1000 = 5, 250, 000, 000 kgs

Cost of Banana = $2.10 per kg

So,

Cost of all bananas = 5, 250, 000, 000 x 2.10 = $ 11,025,000,000 (per year)

Taking a year to be 365 days, let's find the cost for a day:

Since there are 317 million [317,000,000] people in the US, the cost per person every day is:

Rounding to the nearest cent,

Answer:

Brand a price is less than Brand b.

Step-by-step explanation:

given-

two brands of canned dog food are on sale. assume that the cans are the same size. brand a costs $13.60 for eight cans and brand b costs $8.75 for five cans

first-brand a costs $13.60 for eight cans

second- brand b costs $8.75 for five cans

solve first

for 8 cans-->$13.60

then,1 can -->$13.60/8

               =>$1.7

in similar manner we solve for second

for 5 cans-->$8.75

then,1 can -->$8.75/5

               =>$1.75

Brand a price is less than Brand b.

Unit pricing helps consumers compare the prices of packaged goods when those goods aren't sold in equal quantities. It's unit pricing that allows, for example, a shopper to tell at a glance which is the better buy: a 20-pound bag of dog food that sells for $13.95 or a 15-pound bag that sells for $10.69.

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