Explain step by step​

The simplified expression in this problem has the result given as follows:

40.

The expression for this problem is defined as follows:

[tex]\frac{(8^4)^3 \times 5^2 \times 5^3}{8^7 \times (8 \times 5)^4}[/tex]

Applying the power of power rule, which states that we keep the bases and multiply the exponents we, have that:

Hence:

[tex]\frac{8^{12} \times 5^2 \times 5^3}{8^7 \times 8^4 \times 5^4}[/tex]

When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:

[tex]\frac{8^{12} \times 5^5}{8^{11} \times 5^4}[/tex]

When two terms with the same base and different exponents are divided, we keep the bases and add the exponents, hence:

8 x 5 = 40.

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The correct answer to the question is option c) An effect modifier.

A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).

It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.

In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.

An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.

Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.

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The volume of the inscribed cube is equal to twice the cube of the sphere's radius, which is 864 cubic units.

Let the side of the inscribed cube be 's.' The diagonal of the cube is the diameter of the sphere, which is 12 units. Therefore, by using the Pythagorean theorem, we get:

s² + s² + s² = 12²

3s² = 144

s² = 48

The volume of the cube is given by s³, which is 48√3 cubic units.

Now, the volume of the sphere is (4/3)πr³, where r is the radius of the sphere. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the diagonal of the cube, which is s√3. Hence, r = (s√3)/2.

Substituting the value of r in the volume formula, we get:

(4/3)π[(6)(√3)/2]³ = (4/3)π(54√3) = 72π√3 cubic units

Therefore, the volume of the cube is twice the volume of the sphere, which is 864 cubic units.

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Becky is correct if x + y = 180° ,   indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x +  y ≠ 180°.

A cyclic quadrilateral, also known as an inscribed quadrilateral in Euclidean  geometry, is a quadrilateral with all   of its vertices on a single circle.

To determine the size of angle C in terms of x and y, we can use the fact that tangent BC touches the circle ABDE at B.

This means that angle C is equal to the angle formed between the chord AD and the tangent BC at point B.

4.1.1

Since AB || EC, we can use the alternate interior angles theorem to determine the relationship between angles C and A₁.

Angle C is equal to angle A₁ because they are corresponding angles.

Therefore, the size of angle C is y.

4.1.2   - To determine if BCDF is a cyclic quadrilateral

 In order to check if BCDF is cyclic, we need to determine if the opposite angles in the quadrilateral add up to 180° .

Let's consider angle BCD and angle BFD:

Angle BCD is equal to angle B₁ (given) and is represented by x.

Angle BFD is equal to angle A₁ (since BCDF is a cyclic quadrilateral) and is represented by y.

If x + y = 180 degrees, then BCDF is a cyclic quadrilateral.

conclusively , Becky is correct if x + y = 180°, indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x + y ≠ 180°.

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Answer:

x = 8

Step-by-step explanation:

If those two given angles equal each other, then u and v are parallel.

7x - 6 = 5x + 10

2x = 16

x = 8

If x = 8, then lines u and v are parallel.

The best measure of central tendency for Patrick's scores would be the median, which is 72.5.

To determine which measure of central tendency best describes Patrick's scores, let's consider the three main measures: mean, median, and mode.
1. Mean: Calculate the average by adding all scores and dividing by the number of tests.
(70 + 74 + 72 + 71 + 73 + 96) / 6 = 456 / 6 = 76
2. Median: Arrange the scores in ascending order and find the middle value.
70, 71, 72, 73, 74, 96
There are two middle values (72 and 73), so the median is their average: (72 + 73) / 2 = 72.5
3. Mode: Identify the most frequent score.
There is no mode, as all scores occur only once, except for the outlier (96).
The best measure of central tendency for Patrick's scores would be the median, which is 72.5. The median is less influenced by the outlier (96) and provides a more accurate representation of Patrick's typical performance on the science tests.

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35>28

For this problem, just replace x with seven and multiply by four.

35 > 4•7

This should get us to our new equation, 35 > 28

Nina will catch up Kevin in 1 hour.

Given that Kevin has completed 90 miles in the race and Nina completed 15 miles less, Kevin continues the race at a constant rate of 25mph and Nina continues the race at a constant rate of 30mph.

So, Nina covered the distance = 90-15 = 75 miles.

So,

When will finish the race, Kevin has already covered 15 miles,

So, Nina needs to catch Kevin by covering 15 + 15 = 30 miles

So, time taken by Nina cover 30 miles = 30/30 = 1 hours

Hence Nina will catch up Kevin in 1 hour.

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Answer:

The sample size is 30.

The sample mean is $36,900.

The sample standard deviation is $8,250.

The confidence level is 98%.

The critical value for a 98% confidence interval with 29 degrees of freedom is 2.457.

The confidence interval is calculated as follows:

(Sample mean - t-critical value * sample standard deviation / sqrt(sample size), Sample mean + t-critical value * sample standard deviation / sqrt(sample size))

(36,900 - 2.457 * 8,250 / sqrt(30), 36,900 + 2.457 * 8,250 / sqrt(30))

(21,668.25, 52,131.75)

Therefore, a 98% confidence interval for the mean account valuation of the population of customers is $21,668.25 to $52,131.75.

Step-by-step explanation:

Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Answer:

Shown below.

Step-by-step explanation:

The commutative property is a property of binary operations that states that the order of the operands does not affect the result of the operation. In other words, if you swap the order of the operands, you will still get the same result. This property holds true for addition and multiplication but not for subtraction and division.

Therefore, the equivalent expressions in order are 7 × 5, 24 + 10, 1 × 3 and 5 × 7.

When we have two large independent samples from two populations, the difference in the two sample means will follow an approximate normal distribution.

This is due to the central limit theorem, which states that when we have a large enough sample size (typically, greater than 30), the distribution of the sample means will be normal regardless of the underlying distribution of the populations. As the two samples are independent, the difference in means will also be independent. Therefore, we can use the normal distribution to estimate the probability of observing a certain difference in means. It is important to note that this approximation may not hold for small sample sizes, and the underlying distributions of the populations can also impact the shape of the distribution. We can say that the normal distribution approximation is widely used in statistics and hypothesis testing, making it an essential concept for understanding and interpreting data.

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Answer:

-----------------------

The average price Jaffar paid for the 5 books is $17.

To find the total cost of the 5 books, we multiply the average price by the number of books:

Now, we'll add up the prices of the first four books:

Finally, we'll subtract the sum of the first four books from the total cost to find the price of the fifth book:

So, Jaffar paid $18 for the fifth book.

The volume of the solid given is 1073.88 cm³.

Given is a composite solid made up of a cone and a cylinder,

We need to find the volume of the composite solid,

So, to find the same we will add both volumes of both the solids,

V(cylinder) = π × radius² × height

V(cone) = π × radius² × height / 3

So, the volume =

= 3.14 × 6² × 6.5 + 3.14 × 6² × 9/3

= 3.14(6² × 6.5 + 6² × 3)

= 3.14(234 + 108)

= 3.14 × 342

= 1073.88 cm³

Hence the volume of the solid given is 1073.88 cm³.

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Step-by-step explanation:

To find f(8 months), we can use the formula:

f(n) = 6000 - 120n

Substituting n = 8, we get:

f(8) = 6000 - 120(8) = 5160

Therefore, f(8 months) is 5160.

To find f(22 months), we can again use the formula:

f(22) = 6000 - 120(22) = 3480

Therefore, f(22 months) is 3480.

To find f(4 years), we need to convert 4 years to months and then use the formula:

f(4 years) = f(48) = 6000 - 120(48) = 48

Therefore, f(4 years) is 48.

Answer to Khan's questions:

- Is the input in savings dollars? Yes, the initial account balance is given in dollars.

- Will the account be at $4660 in one year? No, we cannot determine this without additional information about the interest rate or other factors that may affect the account balance.

- Will it take 50 months for the account to hit $0? No, we cannot determine this without additional information about the interest rate or other factors that may affect the account balance.

Answer:

the answer would be b and d

Step-by-step explanation:

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Answer:

[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]

[tex]\alpha = 1 \quad \textsf{and} \quad \beta=2[/tex]

[tex]b=-3[/tex]

Step-by-step explanation:

If α and β are roots of x² + bx + c = 0 then the equation must be:

[tex](x -\alpha)(x - \beta) = 0[/tex]

Expanding we get:

[tex]x^2-\beta x - \alpha x + \alpha \beta = 0[/tex]

[tex]x^2-(\alpha +\beta ) x + \alpha \beta = 0[/tex]

Equating the coefficients we get:

[tex]\alpha + \beta=-b[/tex]

[tex]\alpha \cdot \beta=c[/tex]

For an equation with the roots α³ and β³, the sum of the roots can be rewritten in terms of (α + β) and (α·β) using the Sum of Cubes formula, and the Square of Binomials formula:

[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)(\alpha^2-\alpha\beta+\beta^2)\\&=(\alpha + \beta)(\alpha^2+2\alpha\beta+\beta^2-3\alpha\beta)\\&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\end{aligned}[/tex]

Substitute in the expressions for (α + β) and αβ to find the sum of the roots α³ and β³ in terms of b and c:

[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\\&=(-b)((-b)^2-3c))\\&=-b(b^2-3c)\\&=-b^3+3bc\end{aligned}[/tex]

The product of the roots α³ and β³ in terms of c is:

[tex]\alpha \cdot \beta = c[/tex]

[tex](\alpha \cdot \beta)^3 = c^3[/tex]

[tex]\alpha^3 \cdot \beta^3=c^3[/tex]

For a quadratic equation in the form x² + bx + c = 0:

So for x² + bx + c = 0 with roots α³ and β³:

[tex]x^2-(\alpha^3 + \beta^3)x+(\alpha^3 \cdot \beta^3)=0[/tex]

[tex]x^2-\left(-b^3-3bc\right)x+c^3=0[/tex]

[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]

Therefore, the equation with the roots α³ and β³ is:

[tex]\boxed{x^2+\left(b^3-3bc\right)x+c^3=0}[/tex]

Substitute the given value of c = 2:

[tex]x^2+\left(b^3-3b(2)\right)x+2^3=0[/tex]

[tex]x^2+\left(b^3-6b\right)x+8=0[/tex]

If b³ - 6b + 9 = 0, then (b³ - 6b) = -9.

Substitute this into the equation:

[tex]x^2-9x+8=0[/tex]

Factor:

[tex](x-1)(x-8)=0[/tex]

Therefore, the roots of the equation with the roots α³ and β³ are 1 and 8, so the values of α and β are:

[tex]\alpha^3 =1 \implies \alpha = 1[/tex]

[tex]\beta^3=8 \implies \beta=2[/tex]

To find the real roots of b³ - 6b + 9 = 0, substitute the found values of α and β into the expression for b:

[tex]b=-(\alpha + \beta)[/tex]

[tex]b=-(1+2)[/tex]

[tex]b=-3[/tex]

Therefore, the real root of b³ - 6b + 9 = 0 is b = -3.

We can confirm this by substituting b = -3 into the equation:

[tex]\begin{aligned}(-3)^3-6(-3)+9&=-27+18+9\\&=-9+9\\&=0\end{aligned}[/tex]

Using the combination formula, we calculate that there are 133,784,560 different 7-card hands that can be chosen from a standard 52-card deck.

A standard 52-card deck has 52 unique cards, and to find the number of different 7-card hands that can be chosen, we use the combination formula, which is C(52,7). This formula represents the number of ways to choose 7 cards out of a total of 52 cards, where order does not matter.

The formula for C(52,7) is derived by using factorials. For example, 52! represents 52 x 51 x 50 x 49 x 48 x 47 x 46 x ... x 2 x 1, which is the total number of ways to arrange all 52 cards. The denominator, 7! x 45!, represents the number of ways to arrange the 7 chosen cards out of 52, and also the number of ways to arrange the remaining 45 cards that were not chosen.

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Within the relevant range, a curvilinear cost function can be graphed as a curved line. A curvilinear cost function is a cost function where the total cost changes as a function of the level of activity, but not at a constant rate.

This means that as the level of activity increases, the cost per unit may increase or decrease, resulting in a curved relationship between the level of activity and the total cost. In order to determine the optimal level of activity, a manager can use calculus to find the point where the marginal cost equals the marginal revenue.

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a city with more than 100,000 residents located within a metropolitan area but that is not the central city and that has maintained a double-digit growth rate in recent years is known as an "edge city."

A suburban city refers to a city with more than 100,000 residents located within a metropolitan area but that is not the central city. These cities are often characterized by their proximity to a larger city, and they may offer a more suburban or residential feel compared to the central city. Additionally, suburban cities have maintained a double-digit growth rate in recent years due to factors such as increased economic opportunities and a higher quality of life.

Edge cities are urban areas that have emerged on the periphery of major metropolitan areas, often near major highways or other transportation hubs. These cities experience significant growth due to their strategic location, and they attract businesses, retail centers, and housing developments. This leads to a continuous increase in population and rapid expansion, which can result in a double-digit growth rate.

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Desired graph is attached below.

Steps to draw a desired angle are:

If the sum of angle ABD and angle DBC is equal to 105 degrees, then the statement is verified.

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Complete question:

Draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.

Answer:

Step-by-step explanation:

True

False

True

1. True, the legs of a right triangle are connected to the right angle.

2. False, the hypotenuse of a right triangle is a specific side that is opposite to the right angle, and it is always the longest side of the triangle. The other two sides are called legs.

3. True, the side opposite to the right angle in a right triangle is called the hypotenuse.

The answer is B. Data set A in not linear, and data set B is not linear.

We know that the original recipe is for 6 people, and it requires 800g of pineapple, 4 egg whites, and 1/2 lemon.

If Dan uses 2 1/2 lemons instead of 1/2 lemon, that means he's using 5 times as much lemon juice. Therefore, he's likely making 5 times the original recipe.

So, for Dan's pineapple sorbet, he would need:

800g x 5 = 4000g (or 4kg) of pineapple

4 x 5 = 20 egg whites

1/2 lemon x 2.5 = 1 1/4 lemons (but since we can't really use a quarter of a lemon, we'll just say he needs 1.5 lemons)

Therefore, Dan is making pineapple sorbet for 6 x 5 = 30 people.

The length of the segment NO is 17.9

The given parameters are;

Length of side, QP = 9

Length of QO = 14

The length of  segment NO we have to find.

NO² = qo×(qp×qo)

Plug in the values of qo, qp

Which gives NO² =14(9×14)

=322

NO=17.9

Hence, the length of the segment NO is 17.9

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Given the circle below with tangent \overline{NO} NO and secant \overline{QPO} QPO ​ . If QP=9 and QO=14, find the length of \overline{NO} NO . Round to the nearest tenth if necessary. Q