if the angle HMA is a right angle, the measure of angle SMH = 66 degrees, and angle SMH is complementary to angle HME, find the measure of angle SMA

Answer:

C = 1.

Step-by-step explanation:

x^2 - 2x = (x - 1)^2 - 1   so:

x^2 - 2x + C = (x - 1)^2 - 1 + C

So to get a perfect square  C must be 1 ( as -1 + 1 = 0):-

(x - 1)^2 - 1 + 1 = (x - 1)^2

Checking  this:

x^2 - 2x + 1

= (x - 1)(x - 1) which is a perfect square./

After using  the principle of multiplication for calculation. The total amount of time needed to wait in line is 16 minutes.

here,

We need to implement the principle of multiplication .So looking at the question it is given to us that there are 8 cars present in front at the bank drive-through, and the total time taken by the clerk is 2 minutes.

therefore,

Total time needed to wait in line is

= Number of cars in line * Time taken by the clerk

= 8 x 2

= 16 minutes

After using  the principle of  multiplication. The total amount of time needed to wait in line is 16 minutes.

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Step-by-step explanation:

1. have info for adjacent side and hypotenuse

so use; cosine

cos32=x/19

x=cos32×19

=15.9

2. have info for opposite side and hypotenuse

so use; sine

sin63=16/x

x=16/sin63

=95.6

3. have info for opposite side and adjacent side

so use; tangent

tan26=17/x

x=17/tan26

=14.4

4. have info for opposite side and adjacent side

so use tangent

tan42= x/13

x=tan42×13

x=29.8

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

Given:

radius of the pool increases at a rate of 24 cm/min

To Find:

How quickly does the pool's area grow when the radius is 5 cm?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A = πr²-----------------------------(1)

The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

dA/dt =π 2r dr/dt

we have to find  dA/dt    with  dr/dt  = 24 cm/min and  r =  5cm

substituting the values

dA/dt = π 2(5)24

dA/dt =  π 26*8

dA/dt =  π 240

dA/dt =240π

dA/dt = 753.98

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

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Answer:

40.17

Step-by-step explanation:

4 ten: 4 × 10 = 40

17 hundredth: 17 × 0.01 = 0.17

4 ten and 17 hundredth in decimals: 40 + 0.17 = 40.17

On tossing a fair coin 9 times, the probability of no more than 8 heads where at least one toss is heads would be 511/512.

The possibility of an event happening is gauged by probability. Many things are difficult to forecast with absolute confidence. We can only anticipate the likelihood of an event occurring using it. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

How to solve?

total number of possibilities on tossing a coin 9 times= 2^9

number of ways to get all heads = 1/2^9

number of getting at most 8 heads = number of ways of getting one tail

= 1 - 1/2^9

=511/512

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The property states that if J is a subgroup of G such that J = H ∩ K, then for any a ∈ G, Ja = Ha ∩ Ka. This implies that if H and K are subgroups of finite index in G, their intersection H ∩ K is also of finite index.

The property, we need to show that Ja = Ha ∩ Ka for any a ∈ G.

Let x ∈ Ja, then x = ja for some j ∈ J = H ∩ K. Since j ∈ H and j ∈ K, we have x = ja ∈ Ha and x = ja ∈ Ka, which implies that x ∈ Ha ∩ Ka. Hence, Ja ⊆ Ha ∩ Ka.

Conversely, let y ∈ Ha ∩ Ka. Then y ∈ Ha and y ∈ Ka, which means y = ha = ka for some h ∈ H and k ∈ K. Since j = h^-1k ∈ J = H ∩ K, we have y = ha = jk ∈ Ja. Therefore, Ha ∩ Ka ⊆ Ja.

Combining both inclusions, we conclude that Ja = Ha ∩ Ka for any a ∈ G.

Now, if H and K are of finite index in G, it means that both H and K have a finite number of distinct left cosets in G. Since their intersection H ∩ K is a subset of both H and K, it follows that H ∩ K also has a finite number of distinct left cosets in G. Therefore, H ∩ K is of finite index in G.

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The scale of measurement used for the independent variable in a research study is determined by the nature of the variable and the research question. The four scales of measurement are nominal, ordinal, interval, and ratio.

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Answer:

c

Step-by-step explanation:

just took the quiz

Answer:

C

Step-by-step explanation:

Edge2021

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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Answer:

80%

Step-by-step explanation:

64/80 = .8/1

multiply by a hundred and you get 80%

Answer:

The equation is;

y = 200•0.8^x

where y is the number of bears remaining and x is the year number in particular

Step-by-step explanation:

Let us have the rate of decrease as r and we set up an exponential equation

y = I• ( 1 - r)^x

where r is the percentage decrease, I is the initial population = 200 and x is the number of years

For the population after 1 year, we have;

160 = 200( 1 -r)^x

divide both sides by 200

0.8 = (1-r)^1

0.8 = 1 - r

r = 1 - 0.8

r = 0.2

So the equation will be;

y = 200( 1 - 0.2)^x

y = 200•0.8^x

Answer:

1.slope is 2

2.slope is -3/5

3.slope is 1

4.vertical line slope 0 undefined

5.x=-5

6.horizontal line slope 0 undefined

Step-by-step explanation:

Answer:

1) 2 2) -3/5 3) 1 4) Undefined 5) -5 6) 0

Step-by-step explanation:

Therefore, The journal entry for Johnny to record this transaction is Debit: New laptop for $2,500, Credit: Used laptop for $1,000, Credit: Cash for $800, Credit: Gain on exchange for $700. The journal entry for Barry to record this transaction is: Debit: Old equipment for $120,000, Debit: Loss on exchange for $10,000, Credit: New equipment for $100,000, Credit: Cash for $20,000.

When a company exchanges an old model of a laptop for a new model, the exchange lacks commercial substance. Johnny traded a used laptop with a book value of $1,000 (historical cost of $2,500 minus accumulated depreciation of $1,500) and a fair value of $1.200 for a new laptop with a list price of $2,500. Johnny also needs to pay $800 cash to purchase the new model. The journal entry to record the transaction would be as follows:Debit: New laptop for $2,500Credit: Used laptop for $1,000Credit: Cash for $800Credit: Gain on exchange for $700 ($2,500 - $1,800)Barry trades newer used equipment for an older version of the same equipment that lacks commercial substance. The newer equipment that Barry trades away has a book value of $90,000 (historical cost of $140,000 minus accumulated depreciation of $50,000) and a fair value of $100,000. In addition to receiving the older equipment, Barry receives $20,000 in exchange. The journal entry to record the transaction would be as follows:Debit: Old equipment for $120,000Debit: Loss on exchange for $10,000 ($100,000 - $90,000)Credit: New equipment for $100,000Credit: Cash for $20,000.

Therefore, The journal entry for Johnny to record this transaction is Debit: New laptop for $2,500, Credit: Used laptop for $1,000, Credit: Cash for $800, Credit: Gain on exchange for $700. The journal entry for Barry to record this transaction is: Debit: Old equipment for $120,000, Debit: Loss on exchange for $10,000, Credit: New equipment for $100,000, Credit: Cash for $20,000.

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Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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Answer:

\(2\frac{2}{5}\)

\(7\frac{1}{2}\)

Step-by-step explanation:

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Cola need 50 miles to drive to complete his trip.

Option A is true.

What is Distance?

The total movement of an object without any regard to direction is called distance.

Given that;

Cole is taking a 170-mile trip by car.

He drive for 2 hours with an average speed of 60 miles per hour.

Now, Distance cover in 2 hours with speed 60 miles per hour is calculated as;

Since, Distance = Speed x time

Hence, Distance = 60 x 2 = 120 miles.

So, Remaining speed to complete his trip = 170 - 120 = 50 miles.

Hence, Cola need 50 miles to drive to complete his trip.

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Note: Your function is missing some information. It seems your function is

\(f\left(x\right)=\frac{-3}{x}+7\).

So, I am solving the question based on the function \(f\left(x\right)=\frac{-3}{x}+7\),  because it would still solve your query.

Answer:

Please see the explanation.

Step-by-step explanation:

Given the function

\(f\left(x\right)=\frac{-3}{x}+7\)

A function g is the inverse of a function f for y = f(x), x=g(y)

\(y=\frac{-3}{x}+7\)

Replace x with y

\(x=\frac{-3}{y}+7\)

solve for y

\(y=-\frac{3}{x-7}\)

so the inverse of \(f\left(x\right)=\frac{-3}{x}+7\) will be:

\(f^{-1}\:\left(x\right)=-\frac{3}{x-7}\)

Finding the domain of \(f^{-1}\:\left(x\right)=-\frac{3}{x-7}\)

As we know that domain is the set of the possible input values where the function is defined.

so the function domain must be: \(x<7\quad \mathrm{or}\quad \:x>7\)

Therefore,

\(\mathrm{Domain\:of\:}\:-\frac{3}{x-7}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<7\quad \mathrm{or}\quad \:x>7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:7\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}\)

68% of IQ scores are found to be between 90 and 120

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviation from the mean and 99.7% of the data falls within three standard deviation from the mean.

Given mean of 105 and a standard deviation of 15.

68% of data falls within one standard deviation from the mean = mean ± standard deviation = 105 ± 15 = (90, 120)

68% of IQ scores are between 90 and 120

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After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

Answer:

\(a=1\\b=-1\\c=-1\)

Step-by-step explanation:

Standard form:

\(ax^2+bx+c=0\)

Identify the values in:

\(x^2-x-1=0\)

\(a=1\\b=-1\\c=-1\)

A line segment can have one or more points on it. The numerical length of FG is 4

Given that:

\(FG = 3x - 5\)

\(EF = x\)

\(EG = 5x - 8\)

Because point F is on EG, then:

\(EG = EF + FG\)

So, we have:

\(5x - 8 = x + 3x - 5\)

\(5x - 8 = 4x - 5\)

Collect like terms

\(5x - 4x = 8 - 5\)

\(x =3\)

Recall that:

\(FG = 3x - 5\)

Substitute \(x =3\)

\(FG = 3 \times 3 - 5\)

\(FG = 9 - 5\)

\(FG = 4\)

Hence, the numerical length of FG is 4

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Answer:

24.00

You have to add all 4 sides of the figure.

Answer:

26.85 in

Step-by-step explanation:

The circumference of the whole circle of diameter 5 in is C = πd, which here is C = π(5 in), or approximately 5π in.  We take only half of this, since the figure shows a semicircle, not a full circle.  Then the half-circumference is (5/2)π.

To find the perimeter:  add up the lengths forming the perimeter:  

7 in + (5/2)π in + 7 in + 5 in, or:

19 in +  (5/2)π ≈ 26.85 in

The position of the ball at t = 2 seconds is -0.8 meters.

The position of a ball rolling in a straight line is given by the equation x = 2.0 - 3.6t + 1.1t^2, where x is the position in meters and t is the time in seconds. To find the position of the ball at a specific time, we can plug in the value of t into the equation and solve for x.

For example, if we want to find the position of the ball at t = 2 seconds, we can plug in 2 for t and solve for x:

x = 2.0 - 3.6(2) + 1.1(2)^2
x = 2.0 - 7.2 + 4.4
x = -0.8

Therefore, the position of the ball at t = 2 seconds is -0.8 meters.

Similarly, we can plug in any value of t into the equation to find the position of the ball at that specific time.

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9x+7y

x=8 and y=3

9(8)+7(3)

72+7(3)

72+21

=93