From the this year to ten years later, the number of people employed as physician assistants in the country is expected to increase by 47%. The number of people employed as physician assistants today is 47,000 find the predicted number of physician assistances after ten years ?

Answer:

1900

Step-by-step explanation:

1 kg = 1000g

1.2kg = x

1 kgx = 1200 kg.g

1kg. 1kg

x = 1200 g

1 decagram = 10g

40 decagram = x

1 dg.x = 400 dg.g

1 dg. 1 dg

x = 400g

so the total= 1200g +300 + 400g=1900g

without the unit = 1900

Answer:

x = 3√3;

y = 3

Step-by-step explanation:

Use trigonometry:

\( \sin(30°) = \frac{y}{6} \)

Cross-multiply to find y:

\(y = 6 \times \sin(30°) = 6 \times 0.5 = 3\)

Use the Pythagorean theorem to find x:

\( {x}^{2} = {6}^{2} - {y}^{2} \)

\( {x}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27\)

\(x > 0\)

\(x = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} \)

Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

The equation, in standard form, of the parabola that models the values in the table is:

y = (-35/12)x² - (71/3)x + 3

How to find the equation of a parabola?

To find the equation of a parabola that models the values in the table, we can use the standard form of a quadratic equation, which is:

y = ax² + bx + c

where a, b, and c are constants. To determine the values of a, b, and c, we can use the three points given in the table.

When x = -2, f(x) = -7, so we have:

-7 = a(-2)² + b(-2) + c

Simplifying, we get:

4a - 2b + c = -7

When x = 0, f(x) = 3, so we have:

3 = a(0)² + b(0) + c

Simplifying, we get:

c = 3

When x = 4, f(x) = -73, so we have:

-73 = a(4)² + b(4) + c

Simplifying, we get:

16a + 4b + c = -73

We now have three equations with three unknowns (a, b, and c). We can solve this system of equations using substitution or elimination. For simplicity, we will use elimination. Subtracting the second equation from the first, we get:

4a - 2b = -10

Subtracting twice the second equation from the third, we get:

16a + 4b - 6c = -146

Substituting c = 3, we get:

16a + 4b - 18 = -146

Simplifying, we get:

16a + 4b = -128

Dividing by 4, we get:

4a + b = -32

We can now substitute b = -32 - 4a into the first equation to get:

4a - 2(-32 - 4a) + 3 = -7

Simplifying, we get:

12a + 35 = 0

Solving for a, we get:

a = -35/12

Substituting a into the equation 4a + b = -32, we get:

b = -32 - 4a = -32 + 35/3 = -71/3

Therefore, the equation, in standard form, of the parabola that models the values in the table is:

y = (-35/12)x² - (71/3)x + 3

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The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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Answer:

Its 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

make a factor tree, find the product of the prime factors, it will be 12.

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

\(\chi^2 =\frac{20-1}{2500} 68^2 =35.14\)

The degrees of freedom are given by:

\( df = n-1=20-1=19\)

And the p value would be given by:

\(p_v =2*P(\chi^2 >35.14)=0.0268\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true variance for this case is different from 2500

Step-by-step explanation:

Information given

\(n=20\) represent the sample size

\(\alpha=0.05\) represent the confidence level  

\(s^2 =68^2=4624 \) represent the sample variance obtained

\(\sigma^2_0 =2500\) represent the value that we want to test

Null and alternative hypothesis

We want to test if the true variance is 2500, so the system of hypothesis would be:

Null Hypothesis: \(\sigma^2 = 2500\)

Alternative hypothesis: \(\sigma^2 \neq 2500\)

Calculate the statistic  

The statistic would be given by:

\(\chi^2 =\frac{n-1}{\sigma^2_0} s^2\)

Repalcing we got:

\(\chi^2 =\frac{20-1}{2500} 68^2 =35.14\)

The degrees of freedom are given by:

\( df = n-1=20-1=19\)

And the p value would be given by:

\(p_v =2*P(\chi^2 >35.14)=0.0268\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true variance for this case is different from 2500

Answer:

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We are 95% confident that the true population proportion is between 71.6% and 80.4%

The 95% confidence interval for the proportion of all U.S. grown people who would include those  on their list of 10 historic events can be constructed using the formula:

Where:

\(pi\) = sample proportion (76%)

SE = standard error (square root of \(pi(1-pi)/n\))

z = the critical value for a 95% confidence level (1.96)

n = sample size (2025)

Plugging in the values, we get:

\(SE =\sqrt{(0.76(1-0.76)/2025)} = 0.0240\\CI = 0.76 ± (1.96)(0.0240) = (0.716, 0.804)\)

The 95% confidence interval can be interpreted as follows: If we repeated this study many times, 95% of the intervals constructed would contain the true population proportion of all U.S. grown persons who would include on their list of 10 historic events. Based on this sample, we are 95% confident that the true population proportion is between 71.6% and 80.4%.

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How do you get the answer by adding all of the percentages together? (100-10=90-12=79.2-23=56.2-5=51.2)

So if there were 100 applicants, 10% of 100 is 90 so 10 applicants did not meet the business requirements leaving 90. Then about 11 (10.8 exactly) people did not pass the pre-screening assessment. Leaving 79 people, 23% of the 79 people didn’t show up for the interview, 23% of 79 is around 18, and 79-18= 61. Than 5% of the 61 did not pass the background investigation, which is 4 (3.5) 61-4=57, so 57 applicants were left. The company only needs 30 people to hire so automatically you know 100 applicants who applied for the job are too many, use the numbers I gave you and use the same concept to find the exact answer.

\( \huge \purple{\tt{Answer:}} \)

Area of a triangle = \( \sf{{\dfrac{1}{2}} \times base \times height} \)

\( \implies{\dfrac{1}{2}} \times 6 \times height = 36 \)

\(\implies height={ \dfrac{{\bcancel{36}^6}\times{2}}{{ \bcancel6}}} \)

\( \implies height = 12~m \)

Answer:

4.84096e+25

Answer:

Step-by-step explanation:

Answer:

What is the diagram?

Step-by-step explanation:

Answer:

33 degrees

Step-by-step explanation:

31-(-2)=33

Answer:

I can't see the pdf

Step-by-step explanation:

please put the image up

Answer:

B it originally cost 12000

Step-by-step explanation:

the depriciation factor is  0.75^t and the original value was 12000

Answer:

(2) The motorcycle cost $12,000 when purchased.

Step-by-step explanation:

\(V(t)=12000(0.75)^t\)

\(V(0)=12000(0.75)^0=12000\)

\(V(1)=12000(0.75)^1=9000\)

\(V(2)=12000(0.75)^2=6750\)

etc.

⇒ Initial cost = $12,000

⇒ The motorcycle's value is decreasing by 25% each year.

Answer:

32,063.06

Step-by-step explanation:

the formula for compound interest: \(A = P(1+\frac{r}{n})^{nt\\}\)

so to use this you are essentially solving for a.

p is the principle (or initial) amount deposited.

r is the rate (in percent)

n is the number of time periods compounded (like annually, monthly, weekly, or daily)

t is the time period (in years)

In this instance the formula looks like: \(A = 30,000(1+\frac{0.03}{1})^{1*2.25}\)

You then solve for A using the formula. It is important to remember to use the order of operations

Answer:

40 degrees

Step-by-step explanation:

We know the entire angle of ABD is 70 and CBD and ABC are in it.

Since we know one of them (CBD) is 30, we can subtract 30 from 70 to find ABC. This is because the angle of ABC and CBD equal ABD.

30 + x = 70

-30 from both sides

x = 40

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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The exponential function will be equal to y = 20ˣ.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carter shared his post with 10 friends, who each share with only 2 people each day.

The exponential function will be written as,

y = abˣ

y = 10(2)ˣ

y = 20ˣ

Therefore, the exponential function will be equal to y = 20ˣ.

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Answer:

f(x) = 10(2)^x

Step-by-step explanation:

Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.

Answer:

552.5 dollars.

Step-by-step explanation:

The probability that precisely eight cell phone owners used their phones to guide their purchasing decisions is 31%.

Probability measures the ratio of the likelihood of an outcome happening out of possible outcomes.

Probability is depicted as fractions, decimals, or percentages because they show the chance that an expected event occurs in the face of many possible events.

This implies that probability can be zero or 1 but not less than zero or more than 1.

The probability that cell phone owners used their phones for guidance = 58%

The sample size of cell phone owners studied = 15

The probability of 8 phone owners out of 15 using their phones for guidance on purchase decisions = 53% (8/15)

The probability that of 8 from 15 of the 58% cell phone owners using their phones for purchase decisions = 31% (58% x 53%).

Thus, the probability that precisely eight cell phone owners used their phones to guide their purchasing decisions is 31%.

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Yes , the arithmetic sequence ( written as sequences of the form (a , a+k , a+2k , a+3k for some constants a and k ) is a subspace of V .

To determine whether subsets of V in the arithmetic sequences are subspaces of V, we check if they satisfy the three conditions for a subset to be a subspace:

(i) The subset must contain the zero vector.

(ii) The subset must be closed under vector addition.

(iii) The subset must be closed under scalar multiplication.

Let S be a subset of V consisting of arithmetic sequences.

Now we check the three conditions :

(i) We find an arithmetic sequence in S that has all its terms equal to zero. The only arithmetic sequence that satisfies this is the sequence (0, 0, 0, 0, ...), which is in S.

So , the subset "S" contains zero vector.

(ii) Next we need to show that if u and v are two arithmetic sequences in S, then their sum "u + v" is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) and V = (b, b+l, b+2l, b+3l, ...) be two arithmetic sequences in S.

Then, their sum is ⇒ u+v = (a+b, a+k+b+l, a+2k+b+2l, a+3k+b+3l, ...).

This is also an arithmetic sequence,

So , subset "S" is closed under vector addition.

(iii) Next , we show that if U is an arithmetic sequence in S and C is a scalar, then CU is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) be an arithmetic sequence in S, and let c be a scalar.

we get , CU = (ca, ca+ck, ca+2ck, ca+3ck, ...) is also an arithmetic sequence,

So , subset "S" is closed under scalar multiplication.

we see that , S satisfies all three conditions, it is a subspace of V.

Therefore, any subset of V consisting of arithmetic sequences is a subspace of V.

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The given question is incomplete , the complete question is

Let V be the space of all infinite sequences of real numbers , Which of the subsets of V in The arithmetic sequences [i.e. sequences of the form (a , a+k , a+2k , a+3k for some constants a and k] are subspaces of V ?

Answer:

The answer is b

Step-by-step explanation:

Answer:

m∠T = 72°

m∠U = 54°

Step-by-step explanation:

Property of an isosceles triangle,

Opposite angles of two equal sides of an isosceles triangle are equal in measure.

By this property, in the given triangle STU,

Since, ST ≅ TU,

m∠S = m∠U = 54°

Since, sum of interior angles of a triangle is 180°

m∠T + m∠S + m∠U = 180°

m∠T + 54° + 54° = 180°

m∠T = 180° - 108°

m∠T = 72°

Answer: 5

Step-by-step explanation:

8+2=10

10/2=5

Answer:

5!!!!!

Step-by-step explanation:

Divide 10 by 2, the result of which is 5, this is the y coordinate of the midpoint. Put the two coordinates together; the midpoint of (0,2) and (2,8) is (1,5).

There you go an... ANSWER<3

By answering the presented question, we may conclude that D) a > b is equation similarly false since, as seen in B, 0.85a is bigger than b.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

If an is 85% of b, we may express it as:

0.85a = b

Let us now look at each option:

A) a = b is not universally true since b is only 85% of a and not equal to a.

B) a b is also false since b is a portion of a and 0.85a is bigger than b.

D) 20a = 17b is not true, because the equation 0.85a = b shows that 17/20 of an equals b, not the other way around.

D) a > b is similarly false since, as seen in B, 0.85a is bigger than b.

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Answer:

• Potential Roots are: 1, -1, 1/2, -1/2, 2,-2,4, and -4.

• Actual roots: -1 and -2.

• Code piece: H.

Explanation:

Given the polynomial:

Applying the rational Toot theorem:

The constant = 4

• The factors of the constant, p = ±1,±2, and ±4

The leading coefficient = 2

• The factors of the leading coefficient, q = ±1 and ±2.

The potential roots are obtained below:

Potential Roots are: 1, -1, 1/2, -1/2, 2,-2,4, and -4.

Next, find the actual roots by substituting each of the potential roots for x:

From the calculations above, the actual roots are -1 and -2.

Thus, the actual roots are:

The code piece is H.