what will be the 40th term in the sequence defined by an=-12+4(n-2)

Answer:

Yes

Step-by-step explanation:

You can conclude there are 18 horses because although some of the mares might be brown horses, the conjunction "and" implies the mares are in addition to the brown horses.

The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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Answer:

Step-by-step explanation:

1) i think for the first question any probability greater than 0.4 has more likelihood that it will happen

2) mutually exclusive events are ones that cannot occur at the same time as it's impossible e.g. a single coin toss cannot result in you getting heads and tails

Answer:

5.10 people

Step-by-step explanation:

Calculation to Find the standard deviation for the number of people with the genetic mutation

Using this formula

Standard deviation = √ ( n * p * q)

Where,

n = 400

p = .07

q = 100%-7% = 93% or .93

Let plug in the formula

Standard deviation =√400*07*.93

Standard deviation =√26.04

Standard deviation = 5.10 people

Therefore the standard deviation for the number of people with the genetic mutation is 5.10 people.

What we need to memorize when finding the slope is this formula:

\( \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }\)

m here represents the slope. I hope this does not confuse you with line m.

The problem here is that we do not have any given points, but we have a way.

If we notice on the graph, the graph contains or passes through (2,-1) and (-2,1). We can use these points to find the slope. So let these be the following:

\( \displaystyle \large{(x_1,y_1) = (2 ,- 1)} \\ \displaystyle \large{(x_2,y_2) = ( - 2 ,1)} \)

Then we substitute these points in the formula.

\( \displaystyle \large{m = \frac{ 1 - ( - 1)}{ - 2 - 2} }\)

negative × negative = positive.

\( \displaystyle \large{m = \frac{ 1 + 1}{ - 2 - 2} } \\ \displaystyle \large{m = \frac{ 2}{ - 4} } \longrightarrow \boxed{m = - \frac{1}{2} }\)

Since m represents the slope. Therefore, the slope of line m is -1/2

The ∠1 & ∠3 are supplementary angles

What is parallelogram?

A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.

Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180.

Here both lines are parallel and the 3rd line is a intersection of both line.

Hence, The ∠1 & ∠3 are supplementary angles

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Answer: The system of differential equations can be rewritten as a matrix equation:

[x', y']^T = [-4y, -6x]^T

The characteristic equation is obtained by setting the determinant of the matrix [A - λI] equal to 0, where A is the coefficient matrix, λ is an eigenvalue, and I is the identity matrix:

det([A - λI]) = det([-λ -4y; -6x, -λ]) = λ^2 + 24 = 0

Thus, λ = ±2i√6. The general solution to the system is then given by:

x(t) = c1cos(2√6t) + c2sin(2√6t)

y(t) = -2c1sin(2√6t) + 2c2cos(2√6t)

where c1 and c2 are constants determined by the initial conditions. Using the initial condition x(0) = -2, y(0) = -2, we can solve for c1 and c2:

-2 = c1cos(0) + c2sin(0)

-2 = -2c1sin(0) + 2c2cos(0)

c1 = -2

c2 = -2

So the particular solution to the system is:

x(t) = -2cos(2√6t) - 2sin(2√6t)

y(t) = 4sin(2√6t) - 4cos(2√6t)

The critical point (0,0) is a center, as the solution spirals towards the origin as t increases.

Step-by-step explanation:

Why are you cheating... I will report this to your teacher

Answer:

Vc = (π/3)✓17 ≈ 4.12 ft³

Step-by-step explanation:

h = ✓(4²+1²)

h = ✓17

V = πr²h/3

V = π(1)²✓17/3

V = (π/3)✓17 ≈ 4.12

Answer:

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

75% of adults believe that an unattractive smile hurts career success.

This means that \(p = 0.75\)

Suppose that 25 adults are randomly selected.

This means that \(n = 25\)

What is the probability that 15 or more of them would agree with the claim?

This is:

\(P(X \geq 15) = 1 - P(X < 15)\)

In which:

\(P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)\)

14 is below the mean, so we start below and go until the probability is 0. Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189\)

\(P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074\)

\(P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025\)

\(P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007\)

\(P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002\)

\(P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0\)

Then

\(P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297\)

And

\(P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703\)

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Answer:

$3825

Step-by-step explanation:

Answer:

solution,

Summation FX=41+32+30+27+28+42+35+X=235+X

N(total number of items)=8

Mean=33

Now,

\(mean = \frac{summation \: fx}{n} \\ \: \: or \: 33 = \frac{235 + x}{8} \\ or \: 33 \times 8 = 235 + x \\ or \: 264 = 235 + x \\ or \: - x = 235 - 264 \\ or \: - x = - 29 \\ x = 29\)

Hope this helps...

Good luck on your assignment..

Answer:

x = 29.

Step-by-step explanation:

There are a total of 8 numbers so if 33 is the mean then the total value is 33*8

= 264.

So  41+32+30+27+28+42+35+X = 264

235 + X = 264

X = 264 - 235

= 29.

By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Answer:

Test statistic = 1.818

Reject H0

Step-by-step explanation:

H0 : μ = 90

H1 : μ > 90

xbar = 94 ; s = 22 ; n = 100

The test statistic : (xbar - μ) ÷ (s/√(n))

Test statistic = (94 - 90) ÷ (22/√100)

Test statistic = 4 ÷ 2.2

T = 1.818

The critical value :

At α = 0.10

Degree of freedom = n - 1 = 100 - 1 = 99

Tcritical(0.10, 99) = 1.290

Decison region :

Reject H0 if Test statistic > |Tcritical |

1.818 > 1.290

We reject H0

Answer:

-1/8   <----- FRACTION

Step-by-step explanation:

The number of candy still in the bag is the dependent variable, while the independent variable, x, stands for the length of time spent eating, as the number of candies still in the bag relies on the length of time spent eating. A function relating these variables is H(x) = 60 - 5x. So H (10) = 40, meaning there are 40 candies left in the bag.

H(x) = 60 - 5x

H(10) = 60 - 5(10)

H(10) = 60 - 50

H(10) = 10

The independent variable, x, represents the number of minutes eating and the dependent variable is the number of candies left in the bag because the number of candies left depends on the number of minutes eating. This is a linear relationship, meaning that the rate at which the candies are being eaten is constant, so the decrease in the number of candies is proportional to the number of minutes eating. A function relating these variables is H(x) = 60 - 5x. This is a linear equation, with a slope of -5, which means for every minute eating, the number of candies left decreases by 5. So, when x = 10, H(10) = 60 - 5(10) = 60 - 50 = 10, meaning there are 10 candies left in the bag. This function can be used to determine the number of candies left in the bag at any point in time.

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Answer:

(C) A reflection across a horizontal line and a horizontal translation

Step-by-step explanation:

We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.

Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.

Hope this helped!

The arc VQRST spans half the circle, so it measures 180 degrees. It's made up of the minor arcs VQ, QR, RS, and ST, so their measures all add up to 180 degrees.

\((y+7) + (x+11) + 3y + 65 = 180 \implies x + 4y = 97\)

The arc QRS is subtended by a right angle, so it measures 90 degrees. It's made up of arcs QR and RS, so

\((x+11) + 3y = 90 \implies x + 3y = 79\)

Solve for \(x,y\). Eliminating \(x\), we have

\((x+4y) - (x + 3y) = 97 - 79 \implies \boxed{y = 18}\)

Substituting this into either equation, we find

\(x + 4\cdot18 = 97 \implies \boxed{x=25}\)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The number z is equal to 2x + 30

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We are given that one number is x + 40 + x - 10

2(x + 15)

Let the number be z

So, both the input are equal to each other;

z = x + 40 + x - 10 = 2(x + 15)

z = 2x + 30

Hence, the numbers z is 2x + 30.

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Answer:

5,-4

Step-by-step explanation:

-4 + 9 = 5 and 0 -4 = -4 so the answer will be (5,-4)

Answer:

(5,-4)

Step-by-step explanation:

I hope this helps!

a z-test for the proportional difference is the proper hypothesis test.

A hypothesis test can be used to find whether the deviation in proportions impacts the medication's effectivity. We may compare the secondary hypothesis—that the proportions are different—to the null hypothesis.

which states that the dimension of patients who show cut down blood pressure is the same for the two doses of the drug (50 mg and 100 mg).

Popular test statistics like the z-test can be applied to this hypothesis test and other statistical analyses.

\(z = (p1 - p2) / SE\)

where p1 and p2, for the 50 mg and 100 mg doses, respectively, are the sample proportions of patients who show fallen blood pressure, and SE is the standard error of the difference between the proportions.

the samples are assumed to be independent or dependent, impacts the SE formula. The samples in this instance are presumed to be independent because they came from various patients. Consequently, the equation for SE is:

\(SE = \sqrt(p1 \times (1 - p1)/n1 + p2 *\times(1 - p2)/n2)\)

here, the sample sizes for two doses is n1 and n2.

We can compute the z-test statistic based on the sample sizes and proportions and compare the result to a critical value or p-value to decide whether to accept or reject the null hypothesis.

Therefore, a z-test for the proportional difference is the proper hypothesis test.

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

B.

True

Step-by-step explanation:

next time change it to is/are replace of is(are) (⁠~⁠_⁠~⁠;⁠)

In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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Answer:

If f(-5) = 7, then the point P(-5, 7) will be on the graph of f

where -5 is the x-coordinate and 7 is the y-coordinate

Step-by-step explanation:

The calculated value of k on the line is 9

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

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

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

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

\(\pi {r}^{2} \frac{h}{3} \)

Plug the values

\( = 3.14 \times {10}^{2} \times \frac{6}{3} \)

Evaluate the power

\( = 3.14 \times 100 \times \frac{6}{3} \)

Calculate

\( = 628 \: {units}^{3} \)

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

\(v = \frac{1}{3} \times \pi \times {r}^{2} \times h\)

\(let \: r = 10 \: , \: h = 6\)

\(v = \frac{1}{3} \times \pi \times {10}^{2} \times 6\)

\(v = \frac{1}{3} \times \pi \times 600\)

\(v = 200\pi \: {units}^{3} \)

Lets use process of elimination

Step-by-step explanation:

1. The order of the coordinate grid is like the alphabet. a comes before b,  x comes before y.

2. Step 1 This eliminates 3 and 4. So we are left with 2 and 1.

3. It is not 1 because there is no a and b coordinate. There is only a Y and x one.

4. 4 is on the x axis, 6 is on the y axis.

5. Thus, the answer is 2.

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