Hi please help me!! thanks

Answer:

q = - 3.4

Step-by-step explanation:

- 13(q + 4) = 7q + 16 ← distribute parenthesis on left side

- 13q - 52 = 7q + 16 ( subtract 7q from both sides )

- 20q - 52 = 16 ( add 52 to both sides )

- 20q = 68 ( divide both sides by - 20 )

q = - 3.4

x = 70°, y = 30°, z = 20°

Step-by-step explanation:

Right triangle have a total internal angle of 180°.

x = 180° - 110°

= 70°

z = 180° - 90° - x

= 180° - 90° - 70°

= 20°

y = 180° - 40° - 90° - z

= 180° - 40° - 90° - 20°

= 30°

The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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Scenario 1: At least one ball is red.

In this scenario, we have four possible outcomes: RR (both red), RB (one red and one blue), BR (one red and one blue), and BB (both blue). Since we know that at least one ball is red, the outcome BB is not possible. Therefore, we only need to consider the outcomes RR, RB, and BR.

Out of the three possible outcomes, only one outcome is favorable (RR), where both balls are red. Hence, the probability that both balls are red, given that at least one is red, is 1/3.

Scenario 2: A ball is picked at random and it is painted red.

In this scenario, we assume that one ball has been randomly chosen and it is painted red. Now, we need to consider the two possible outcomes: RR (both red) and RB (one red and one blue).

Out of the two possible outcomes, one outcome is favorable (RR), where both balls are red. Hence, the probability that both balls are red, given that a ball is randomly picked and painted red, is 1/2.

To summarize:

The probability that both balls are red, given that at least one is red, is 1/3.

The probability that both balls are red, given that a ball is picked at random and it is painted red, is 1/2.

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The required probability that X is less than 16 is approximately 0.15866 or 15.86%.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - μ) / σ

In this case, X has a mean of 25 and a standard deviation of 9,

Z = (16 - 25) / 9
z = -1

To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.

P(Z < -1) ≈  0.15866

Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.

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Answer:

D

Step-by-step explanation:

come on, you need to know your own measurement system.

there are 12 inches in a foot.

and there are 3 ft (and therefore 36 inches) in a yard.

now you get a glimpse on why the metric system of the rest of the world is so much easier to understand, where everything is related to other units by factors of 10.

anyway, the stream is 4 1/4 yards wide.

the log is 11 ft long.

11 ft = 11/3 = 3.666666... = 3 2/3 yards.

so, the log is definitely too short. by how much ?

4 1/4 yards = 4×36 + 36/4 in = 144 + 9 = 153 in

3 2/3 yards = 3×36 + 2×36/3 in = 108 + 24 = 132 in

the difference is

153 - 132 = 21 in = 1×12 + 9 = 1 ft 9 in

the log is too short by 1 ft 9 in.

If \($x$\) is an element of the set \($\{ -1, 1, 2 \}$\) and \($y$\) is an element of \($\{ -2, -1, 0, 1, 2 \}$\), the number of distinct values of \($x^y$\) that are positive is 5.

When the base is positive, the exponent produces positive powers.

Now, let's evaluate the power for each possible combination of \($x$\) and \($y$\):

For \($x = -1$\) and \($y$\) being an even number, we get a positive power. Here are the possible even values for \($y$\):
\($y = -2$\) and \($y = 0$\).  Therefore, \($x^y$\) is positive for two possible combinations: \($(-1)^{-2} = 1$\) and \($(-1)^{0} = 1$\).

For \($x = 1$\) and any value of \($y$\), the power of \($x$\) is always positive, and the value of \($x$\) is always 1. Therefore, there's only one possible combination: \($1^y = 1$\).

For \($x = 2$\) and \($y$\) being an even number, we get a positive power. Here are the possible even values for \($y$\):
\($y = -2$\) and \($y = 0$\). Therefore, \($x^y$\) is positive for two possible combinations: \($2^{-2} = 1/4$\) and \($2^{0} = 1$\)

For \($x = 2$\) and \($y$\) being an odd number, we get a negative power. Here are the possible odd values for \($y$\):
\($y = -1$\) and \($y = 1$\). Therefore, \($x^y$\) is positive for zero possible combinations.

Therefore, the total number of distinct values of \($x^y$\) that are positive is \($2+1+2 = 5$\).

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Answer:

9.36 / 0.52 = 18

Step-by-step explanation:

Divide them.

To get it why radians  have fractional answers, one can use the unit of a circle .  the unit circle could be a circle with a radius of 1, centered at the root of a coordinate plane. To measure points in radians on the unit circle, we measure the  arc length of the comparing other part of the circle, as shown within the image attached:

Radian measures angles based on arc length equal to the radius of a circle, resulting in fractions for non-whole arcs. The unit circle has a radius of 1 and is centered at the origin.

This explains why radians can be fractional. To measure angles in radians, we use arc length on the unit circle. Most angles correspond to fractions of a full circle, like π/2 for a quarter circle.

The angle in radians for one-eighth of a circle is approximately 0.79 (π/4), as most circle arcs are not exact multiples of the radius. Most circle arcs cannot be expressed as a whole number of radii.

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The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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After taking the common, the factored form of \(27x^3-64\) is \((3x-4)(9x^2+12x+16)\).

In the given question, we have to find the factored form of \(27x^3-64\).

The following is how we factor the GCF out of a polynomial:

(1) Determine the polynomial's GCF for each term.

(2) Present each term as the GCF and another factor's product.

(3) To factor out the GCF, use the distributive property.

To solve this question we use the formula \((a^3-b^3) = (a-b)(a^2+ab+b^2)\)

We can write \(27x^3-64\) as

\(27x^3-64\) = \((3x)^3-(4)^3\)

\(27x^3-64\) = \((3x-4)((3x)^2+3x\cdot4+(4)^2)\)

\(27x^3-64\) = \((3x-4)(9x^2+12x+16)\)

Hence, the factor form of \(27x^3-64\) is \((3x-4)(9x^2+12x+16)\).

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The complete question is:

What is the factored form of \(27x^3-64\)?

Answer:

b

Step-by-step explanation:

Real-world problem: A store is having a sale on a particular item, where the original price of the item is y dollars. The store advertises that the sale price is $2 less than the original price.

Represent this situation with the inequality y - 4 < 2. To solve the inequality, we add 4 to both sides to isolate the variable: y - 4 + 4 < 2 + 4, y < 6. The solution to the inequality is y < 6, which means that the original price of the item must be less than $6 for the sale price to be $2 less than the original price.

In this situation, all values in the solution make sense. Any value of y that is less than 6 would result in a sale price that is $2 less than the original price. For example, if y is 5, the sale price would be 5 - 2 = 3, which is $2 less than the original price.

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Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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The value of x is 10.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given;

Base=6

Perpendicular=8

Now

x^2=6^2+8^2

X^2=36+64

X^2=100

x=10

Therefore, by pythagoras theorem the answer will be 10.

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Answer:

70 sq. in

Step-by-step explanation:

Area of the figure

= ( 10 x 5 ) + ( 5 x 4 )

= 50 + 20

= 70

= 70 sq. in

Ella has 5.7 pounds of flour, and needs 0.6 of a pound of flour for each cake. This mean that she can bake a total of 9 cakes.

Step 1: Ella has 5.7 pounds of flour

Step 2: Each cake requires 0.6 of a pound of flour

Step 3: 5.7/0.6 = 9.5 (rounded down to 9)

Step 4: Ella can bake 9 cakes

Ella has 5.7 pounds of flour which she wants to use for baking cakes. Each cake requires 0.6 of a pound of flour, so to figure out how many cakes she can make, we need to divide the amount of flour she has by the amount of flour needed for one cake. 5.7/0.6 = 9.5 (rounded down to 9), so Ella can bake 9 cakes. This is because the 0.5 of a pound of flour leftover is not enough to make an entire cake, so it is discarded. This means that Ella can make 9 cakes with the 5.7 pounds of flour she has.

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Answer:

Step-by-step explanation:

:(

The sample size is enough because both np and n(1 - p)  are greater than 10.

Given,

Number of people using a computer in US = 81

Sample size, n = 36

Number of hours people use computer in a week = more than 20 hours

We have to find that the given sample size is enough to compute a confidence interval.

For that we have to find np and n(1 - p) first.

Here,

n = 36

p = 20

Then,

np = 36 x 20 = 720

n(1 - p) = 36 x (1 - 20) = 36 x 19 = 684

That is,

The sample size is enough because both np and n(1 - p)  are greater than 10.

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The given question is incomplete. Completed question is given below;

A study was conducted in order to estimate the proportion of U.S. adults that use a computer at home more than 20 hours a week. Suppose 36 out of a random sample of 81 adults use a computer at home more than 20 hours a week.

The drive-thru is able to estimate their wait time more consistently will be Fast Chicken, because it has a smaller IQR.

In descriptive statistics, the interquartile range tells you the spread of the middle half of the distribution. Quartiles segment any distribution that’s ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of the data set.

The correct option here is Fast Chicken, because it has a smaller IQR (Interquartile Range). IQR is the difference between the third quartile and the first quartile, which is represented by the box in the box plot. In this case, the IQR for Fast Chicken is 14.5 - 10 = 4.5, while the IQR for Super Fast Food is 15.5 - 8.5 = 7. A smaller IQR indicates that the data is more consistent and less spread out.

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The top priority during physical activity in the classroom is the safety and well-being of the students.

Ensuring a safe environment for physical activity helps prevent injuries and promotes the overall health and engagement of the students.

1. Supervision: Adequate adult supervision should be provided to monitor the students' activities, ensuring they are engaged in safe and appropriate physical exercises.

2. Proper Warm-up and Cool-down: Encouraging students to perform warm-up exercises before engaging in more vigorous activities and cool-down exercises afterward helps prevent injuries and promotes proper muscle recovery.

3. Suitable Physical Activities: The chosen physical activities should be age-appropriate, taking into account the students' physical abilities and limitations. Activities should be designed to minimize risks and promote participation for all students.

4. Clear Instructions and Demonstration: Teachers should provide clear instructions and demonstrate proper techniques for exercises or activities to ensure students understand how to perform them safely and effectively.

5. Equipment and Environment Safety: Regular inspection of equipment and ensuring the physical environment is free from hazards (such as tripping hazards or obstacles) is essential for maintaining a safe setting.

6. Individual Needs and Modifications: Teachers should consider any individual needs or limitations of students, such as physical disabilities or health conditions, and make necessary modifications or adaptations to ensure their safety and inclusion.

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the top priority during physical activity in the classroom is?

Answer:

\( \frac{2}{35} \)

Step-by-step explanation:

\( \frac{ \binom{1}{1} }{ \binom{7}{1} } \times \frac{ \binom{2}{1} }{ \binom{5}{1} } = \frac{2}{35} \)

of course it can easily be simplified, but the logic is shown here!

first you have to draw 1 checker marble out of the seven marbles.

at the top is the ideal draw where you draw the one checker marble out of that one, and the bottom is all the options to draw 1 marble out of the 7 marbles.

3 is the prime number.

again, at the top you draw obe 3 out of the two, and the bottom is all the options to draw one out of the five numbers.

First, we have to acknowledge that the marble draw's outcome is independent from the card being drawn.  Because of this independence, we can multiply the two individual probabilities.

For the marble, there are 7 outcomes (7 marbles we could draw) and only 1 of which is checkered  We have a 1/7 chance of picking a checkered marble.

For the cards, there are 5 possible outcomes (5 cards we could drawa) and 2 are prime (there are two "3" cards).  We have a 2/5 chance of drawing a card with a prime number.

For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:

   1/7 · 2/5 = 2/35

We have a 2/35 (about 5.714%) chance of drawing a checkered marble and then picking a card with a prime number.

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Treats remain = 1 pound

amount bringed to school = 0.6 = 6/10 =3/5

Multiply the treats remain (1 pound )

6/10 X 1 = 3/5 x1 = 3/5

The total utility of 4 units is 50 and the marginal utility is 5

Total utility is the sum of satisfaction that is derived from the consumption of units of a good or service.

Total utility can be determined by adding the marginal utility of each unit that is consumed.

Total utility of consuming 4 units = marginal utility of the first unit + marginal utility of the second unit + marginal utility of the third unit + marginal utility of the fourth unit  

20 + 15 + 10 + 5 = 50

Marginal utility is the change in total utility when consumption increases by unit. Marginal utility is 5

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Answer:

minimum area: 30.40 cm²

maximum area: 30.52 cm²

Step-by-step explanation:

Answer:

14.6

Explanation:

It's pretty simple if you use a calculator, have a nice day and good luck with your work! <3