Which expression is equivalent to (65. 85)3?

Answer:$6.11 per bag

Step-by-step explanation: The total of both the apples and ice cream is 55.68. Since we’re just trying to find the total price of apples, we’ll subtract the total price of ice cream. 55.68-6.80=48.88. Now we’ll divide $48.88 by 8, since there are 8 bags. That leaves us with $6.11

We can say with 90% confidence that the increase in proportion of people satisfied with their financial situation is between 1.05% and 6.71%.

To calculate the confidence interval for the increase in proportion of people satisfied with their financial situation, we need to first calculate the proportions for both years:

Proportion in year 1 = 478/2038 = 0.2342
Proportion in year 2 = 537/1967 = 0.2730

The increase in proportion is:
0.2730 - 0.2342 = 0.0388

To calculate the confidence interval, we can use the formula:
CI = (point estimate ± (critical value x standard error))

The point estimate is the increase in proportion we just calculated: 0.0388

The critical value can be found using a z-table for a 90% confidence level. The z-value for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:
sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

where p1 and n1 are the proportion and sample size for year 1, and p2 and n2 are the proportion and sample size for year 2.

Plugging in the values, we get:
SE = sqrt[(0.2342(1-0.2342)/2038) + (0.2730(1-0.2730)/1967)] = 0.0174

Now we can plug in all the values to get the confidence interval:
CI = (0.0388 ± (1.645 x 0.0174)) = (0.0105, 0.0671)

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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To find the equation of the regression line for the given data, we need to use a statistical software or a calculator. Once we have the equation, we can plot the data on a scatter plot and draw the regression line.

     Using the regression equation, we can predict the value of y (girth) for each of the given x-values (length). However, if the x-value is not within the range of the observed data, the prediction may not be meaningful. For example, if x = 140 cm or x = 172 cm are outside the range of the observed lengths, the predicted girth may not be accurate. On the other hand, if x = 164 cm or x = 158 cm are within the range of the observed lengths, the predicted girth may be more reliable.
Overall, regression analysis helps us understand the relationship between two variables and make predictions based on that relationship. In this case, we can use the regression equation to estimate the girth of harbor seals based on their length, but we need to be mindful of the limitations of the data and the prediction.

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Answer:

A. (x - 3)² + (y + 2)² = 16

Step-by-step explanation:

The formula for a circle plotted on the Cartesian coordinate system is:

\((x - a)^2 + (y - b)^2 = r^2\)

where \((a,b)\) is the center of the circle, and \(r\) is the length of the circle's radius.

Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:

\((x - 3)^2 + (y - (-2))^2\)

which can be simplified to:

\((x - 3)^2 + (y + 2)^2\)

The radius of the circle is given as 4, so we know that the right side of the equation is:

\(4^2\), which is the same as \(16\).

Finally, to answer this question, we can put the two sides of the equation together to get:

\((x - 3)^2 + (y + 2)^2 = 16\)

Answer:

the last one

Step-by-step explanation:

Answer:

\(52 \leqslant h \leqslant 60\)

Step-by-step explanation:

Add and subtract 4 to and from 56

Answer:

The Answer is: C.120

Answer:

∠ RST = 120°

Step-by-step explanation:

∠ RST = ∠ RSU + ∠ UST , substitute values

6x + 12 = 78 + 3x - 12

6x + 12 = 3x + 66 ( subtract 3x from both sides )

3x + 12 = 66 ( subtract 12 from both sides )

3x = 54 ( divide both sides by 3 )

x = 18

Thus

∠ RST = 6x + 12 = 6(18) + 12 = 108 + 12 = 120°

The probability of selecting a short term resident at random from this group is 7/10 or 0.7. This is because there are 7 short term residents out of a total of 10 residents in the group.

The probability of selecting a resident who does not support the homeless shelter at random from this group is 3/10 or 0.3. This is because there are 3 residents who do not support the homeless shelter out of a total of 10 residents in the group.

The probability of selecting a long term resident who supports the homeless shelter at random from this group is 1/10 or 0.1. This is because there is only 1 long term resident who supports the homeless shelter out of a total of 10 residents in the group.

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The triangle ABC is right angled triangle as product of slope of line AB and line AC is equal to -1.

Slope of line AB = 4 /6

Slope of line AC = - 3/2

Slope of line BC = -5/12

Two lines are perpendicular to one another when the product of their slopes is equal to -1.

Slope of line AB × Slope of line AC

= ( 4/6 ) × ( -3/2 )

= (-12 / 12 )

= -1

Thus, the sides AB and AC are perpendicular.

This implies that ,

Triangle ABC is a right triangle.

Therefore, the product of the slope of line AB and AC is -1 and triangle ABC is right triangle.

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Answer:

2. multiply 3/4 by 8

3/4 ÷ 1/8

Copy dot flip

3/4 * 8/1

24/4

6

Click

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

you do KFC or KCF

so 3/4 times 8/1

which the answer is 24/4 which is reduced to 6

hope this helps

Answer:

3/50

Step-by-step explanation:

There are 5 + 4 + 2 + 6 + 3 = 20 marbles in the bag

P(draw a black) = 6/20 = 3/10

If the black marble is replaced, then there are 20 marbles in the bag again.

P(draw a blue) = 4/20 = 1/5

P(draw a black and blue with replacement) = (3/10)(1/5) = 3/50

The next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

To find the time at which all three lights will flash at the same time, we need to find the LCM (Least Common Multiple) of the given times.

Prime factorizing each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

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The area of the rectangle is increasing at a rate of 122cm²/s if the length of the rectangle is 11 cm and the width is 9 cm.

The area of a rectangle can be described as the product of the length and width of that rectangle, therefore;

Area = L × W

Here L represents length and W represents the width

Now by differentiating using the product rule;

dA/dt = (dL/dt)(W) + (dW/dt)(L)

As the length is 11 cm and the width is 9 cm and the length is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s; substituting these values in the equation;

dA/dt = (5)(9) + (7)(11)

dA/dt = 45 + 77

dA/dt = 122

Hence,  the area of the rectangle is increasing at the rate of 122cm²/s.

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Answer:

It will drop 16.875 degrees

Step-by-step explanation:

3.75 × 4 = 15

.5 × 3.75 1.875

Answer:

-16.875

Step-by-step explanation:

This equation is quite simple and will only require one equation to solve. This is the equation,

-3.75×4.5=-16.875

The final answer is -16.875

Answer:

D

Step-by-step explanation:

Answer:

the answerr is i9 dont know haha bum

Step-by-step explanation:

hahay

Answer:

B. 2x + y = 8

Step-by-step explanation:

y = -2x + 5 matches with 2x + y = 8, as they have same slope of "-2".

There you go, it is the second equation with y = -2x + 5.

The proof shows that if the premises (x > 1), a = 1, y = x, y = y – a, (y >\(0 ^ x\) > y) are true, then the conclusion (x > 1) a = 1; y = x; y = y – a; (y > \(0 ^ x\) > y) is also true. The proof also shows the logical relationship between the premises and the conclusion.

To prove that ⊢ (x > 1) a = 1; y = x; y = y – a; (y >\(0 ^ x\) > y), we need to show that the given statement is a valid formula using the axioms of propositional logic and the rules of inference.

Firstly, let's understand the given statement.

(x > 1) a = 1;

y = x;

y = y – a;

(y > 0 ^ x > y)

Here,
(x > 1) is a premise which states that x is greater than 1.
a = 1 is a statement that sets the value of a as 1.
y = x sets the value of y as x.
y = y – a subtracts the value of a from y and updates the value of y.
(y > \(0 ^ x\) > y) is a conjunction of two predicates which states that y is greater than 0 and x is greater than y.

Now, let's use the rules of inference to prove that the given statement is a valid formula.

Proof:
1. (x > 1) (Premise)
2. a = 1 (Premise)
3. y = x (Premise)
4. y = y - a (Premise)
5. y > 0 (Premise)
6. x > y (Premise)
7. y - a > 0 (Subtraction, 5, 2)
8. x > y - a (Substitution, 6, 2, 4)
9. y > a (Subtraction, 3, 2)
10. y > \(0 ^ y\) > a (Conjunction, 5, 9)
11. y > \(0 ^ y\) - a > 0 (Conjunction, 7, 9)
12. y > \(0 ^ x\) > y (Conjunction, 8, 10)
13. (x > 1)

a = 1;

y = x;

y = y – a;

(y > 0 ^ x > y)

Therefore, we have proved that the given statement is a valid formula using the rules of inference and axioms of propositional logic.

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The equation of a tangent line to a curve is used to find the slope of the curve at a specific point. The slope of a curve is calculated by finding the first derivative of the curve. The slope of the curve at a specific point is equal to the slope of the tangent line at that point.For question 3: f(x)=2x³ +5x² +6, at (-1,9).

We will plug in the x and y values of the point (-1, 9) and the slope value to get the equation of the tangent line.y - y1 = m(x - x1)y - 9 = (6(-1)² + 10(-1))(x + 1)y - 9 = (-4)(x + 1)y - 9 = -4x - 4y = -4x + 5For question 4: f(x) = 4x - x², at (1, 3)To find the slope of the curve at (1, 3), we will take the derivative of the function f(x).f(x) = 4x - x²f’(x) = 4 - 2xNow that we have found the slope, we can use the point-slope form to find the equation of the tangent line.y - y1 = m(x - x1)y - 3 = (4 - 2(1))(x - 1)y - 3 = 2(x - 1)y - 3 = 2x - 2y = 2x - 6In conclusion, The equation of the tangent line, in slope-intercept form, to the curve f(x)=2x³ +5x² +6 at (-1,9) is y = -4x + 5 and the equation of the tangent line, in slope-intercept form, to the curve f(x) = 4x - x² at (1, 3) is y = 2x - 6.

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The equation of the tangent line to the curve f(x) = 2x³ + 5x² + 6 at (-1, 9) is y = -4x + 5.The equation of the tangent line to the curve f(x) = 4x - x² at (1, 3) is y = 2x + 1.

To find the equation of the tangent line to a curve at a given point to find the derivative of the function and evaluate it at the given point.

Curve: f(x) = 2x³ + 5x² + 6, Point: (-1, 9)

The derivative of the function f(x)

f'(x) = d/dx(2x³ + 5x² + 6)

= 6x² + 10x

The slope of the tangent line at x = -1 by evaluating the derivative at x = -1

f'(-1) = 6(-1)² + 10(-1)

= 6 - 10

= -4

The slope of the tangent line is -4 the point-slope form of a line (y - y₁ = m(x - x₁)) to find the equation of the tangent line.

y - 9 = -4(x - (-1))

y - 9 = -4(x + 1)

y - 9 = -4x - 4

y = -4x + 5

Curve: f(x) = 4x - x² Point: (1, 3)

The derivative of the function f(x)

f'(x) = d/dx(4x - x²)

= 4 - 2x

The slope of the tangent line at x = 1 by evaluating the derivative at x = 1

f'(1) = 4 - 2(1)

= 4 - 2

= 2

The slope of the tangent line is 2. Using the point-slope form of a line find the equation of the tangent line.

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

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Answer:

1.74 L.

Step-by-step explanation:

Josey has already consumed 700 milliliters of water.

700 mL = 0.07 L

It is recommended that an adult drink 64 fluid ounces of water every day.

64 fluid ounces = 1.81 L (As 1 fluid ounce = 0.0284 L)

We need to find how many more liters he drinks today.

More = 1.81 L - 0.07 L

= 1.74 L

So, 1.74 L more water he drink today.

Q = 180 ( 1.474) ^ t

This in in the form

y = a e ^ (kt)

180 is the initial value

a = 180

1.474 ^t = e^k ^ (t)

This means that e^k = 1.474

Taking the ln of each side

ln (e^k) = ln ( 1.474)

k = ln ( 1.474)

b = 1.474 which is the growth factor

b =1+r

1.474 = 1+r

r = .474

If they want r as a percent

r = 47.4 %

Answer:

36$

Step-by-step explanation:

5x4=20   4x9=36  there for it's 36$

The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c.  m² -3m + 2 = 0.

The equation is equal to,

(x² - 5)² - 3x² + 15 = -2

let the value of m be equals to x² - 5.

Simplify the equation we have,

⇒ ( x² - 5 )² - 3x² + 15 = -2

Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,

⇒ ( x² - 5 )² - 3 (x² - 5 )  = -2

Now replace x² - 5 by m to get the equivalent equation,

⇒ ( m )² - 3 (m ) = -2

⇒ m² -3m + 2 = 0

Therefore, the equivalent equation to the given equation is written as option c.  m² -3m + 2 = 0.

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The corresponding side in the smaller triangle is 10 cm.

When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity.

Given that, the ratio of similitude in two similar triangles is 3:1. the side in the larger triangle measures 30 cm, we are asked to find the measure of the corresponding side in the smaller triangle.

Let the corresponding side in the smaller triangle be x,

Since, the ratio similitude is 3:1, therefore, the ratio of the corresponding sides of both the triangle will be in same ratio,

Therefore,

1 / 3 = x / 30

x = 30 / 3

x = 10

Hence, the corresponding side in the smaller triangle is 10 cm.

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A and C because it asks which word is in the square and pentagon, it is the a and the c

Answer:

8.26

Step-by-step explanation:

1. to do this you have to write down the two numbers, one under the other, with the decimal points lined up.

2. you also have to add zeros so the numbers have the same length.

3. and then subtract normally, remembering to put the decimal point in the answer.

\(\frac{f}{g}(2) = \frac{2}{11}\\\)

\(\frac{f}{g}(2) = \frac{f(2)}{g(2)} \\ \frac{f}{g}(2) = \frac{(2)^2}{5(2)^2 +2} \\ \frac{f}{g}(2) = \frac{4}{5(4) +2} \\ \frac{f}{g}(2) = \frac{4}{20 +2} \\ \frac{f}{g}(2) = \frac{4}{22} \\ \frac{f}{g}(2) = \frac{2}{11}\)

Solution:

Given that a committee of 4 teachers and 3 students is to be formed from 12 teachers and 35 students, we have

Recall that:

This gives:

Hence, the number of committees that can be formed is

Answer:

\(x=\frac{dc-by}{a}\)

Step-by-step explanation:

\(\frac{ax+by}{c}=d\\\\ax+by=dc\\\\ax=dc-by\\\\x=\frac{dc-by}{a}\)