Both Susana and Greg love to collect stamps. Greg has 70 stamps and Susana has 50
stamps How many more stamps does Susana have than Greg?

The number of ways integer points can be assigned to the 12 problems, given that the total points is 100 and each problem is worth at least five points, can be calculated using a combinatorial approach.

To determine the number of ways, we can use the concept of stars and bars, which is a combinatorial technique used to distribute indistinguishable objects into distinguishable groups. In this case, the stars represent the total points (100) and the bars represent the dividers between the problems.

Since each problem is worth at least five points, we can consider a minimum of five points already assigned to each problem. This means we need to distribute the remaining points (100 - 12*5 = 40 points) among the 12 problems.

Using the stars and bars approach, we have 40 stars (representing the remaining points) and 11 bars (representing the dividers between the 12 problems). The number of ways to arrange these stars and bars is equivalent to the number of ways to assign points to the problems.

The answer, therefore, can be calculated using the formula for combinations with repetition: C(n + k - 1, k - 1), where n is the number of stars (40) and k is the number of bars (11).

Hence, the number of ways to assign integer points to the problems is C(40 + 11 - 1, 11 - 1) = C(50, 10).

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Answer:I think its multiply

Step-by-step explanation: 90 x 2 = 180

Answer:

3(2g-6h), -2×(-3g+9h)

Step-by-step explanation:

The expressions equivalent to 6g-18h could be: (since you didn't give any choices to choose from)

3(2g-6h) and,

-2 × (-3g+9h)

Answer: 11.3 or 11 if you are to round to nearest whole number.

Step-by-step explanation:

Take the problem step by step.

You know she has the monthly fee and a fee for each gigabyte of data she stores in her house.

Take how much she paid and Subtract the monthly fee from it since it has been a month.

$60.95 - $14.95 = $36

Now take that answer and divide it by the cost of each gigabyte to see how many she used that month.

$65 / $5.75 = 11.30434743, which rounds to 11.3 or 11 if you are to round to nearest whole number.

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

1.68

Step-by-step explanation:

log723.7=2.86

multiplication in log is addition so 2.86+

log0.0667=-1.18

so 2.86+-1.18=1.68

Answer:

$378

Step-by-step explanation:

(9000 x 0.70%) * 6 = 378

Given tan(x)=24/25 (in quadrant 1), the value of sin(2x) is 2352 / 15625.

It should be noted that tan(x) = sin(x) / cos(x)

Given tan(x) = 24/25, we can represent it as:

24/25 = sin(x) / cos(x)

cos²(x) + sin²(x) = 1

Since we're in quadrant 1, both sin(x) and cos(x) are positive. Let's solve for cos(x):

cos²(x) + (24/25)² = 1

cos²(x) + 576/625 = 1

cos²(x) = 1 - 576/625

cos²(x) = 49/625

Taking the square root of both sides:

cos(x) = sqrt(49/625)

cos(x) = 7/25

Now that we have cos(x), we can find sin(x) using the given equation:

24/25 = sin(x) / (7/25)

Multiplying both sides by (7/25):

(7/25) * (24/25) = sin(x)

168/625 = sin(x)

Now, we have sin(x) and cos(x), and we can use double angle formula to find sin(2x):

sin(2x) = 2 * sin(x) * cos(x)

Substituting the values we found:

sin(2x) = 2 * (168/625) * (7/25)

sin(2x) = (2 * 168 * 7) / (625 * 25)

sin(2x) = 2352 / 15625

Therefore, sin(2x) = 2352/15625.

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Answer:

x < -7 or x > 2

Step-by-step explanation:

The solution includes the interval from negative infinity to -7, not including -7. That means

x < -7

The solution also includes the intervals from 2 to infinity, not including 2. That means

x > 2

Answer: x < -7 or x > 2

Some alkenes have geometric cis-trans isomers because of the presence of a double bond between two carbon atoms. In a carbon-carbon double bond, the carbon atoms are connected to two different groups of atoms, which can be oriented differently in space. In the cis configuration, the two substituent groups on each carbon atom are on the same side of the double bond, while in the trans configuration, the two substituent groups on each carbon atom are on opposite sides of the double bond.

The cis-trans isomerism arises due to the restricted rotation around the carbon-carbon double bond. In the case of cis isomers, the substituent groups are too bulky to rotate around the double bond, and they remain on the same side of the double bond. In contrast, in the trans isomers, the substituent groups are oriented on opposite sides of the double bond, which allows them to rotate freely around the bond.

The presence of cis-trans isomers has important consequences for the physical and chemical properties of alkenes, including their reactivity, solubility, and melting points. The two isomers can have different properties and can exhibit different biological activities, making them important targets for drug design and synthesis.

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Rainfall decreases as latitude increases between thirty and sixty degrees latitude is the best description of the rainfall trend.

At thirty degrees latitude, the Intertropical Convergence Zone (ITCZ) is located, which is a band of low pressure that circles the Earth near the equator.

This zone experiences high precipitation due to the rising and falling of air masses caused by the warm equatorial waters. As we move away from the equator towards sixty degrees latitude, the ITCZ shifts northward and the land and sea temperatures decrease, resulting in less precipitation and less humidity.

This trend is known as the latitudinal rainfall gradient, which states that precipitation decreases as latitude increases. This can be observed in the subtropical regions such as the Mediterranean, the western United States, and the southern parts of Africa, among others.

Also, the trade winds blowing from east to west towards the equator, which are prevailing winds in the tropics, push the clouds and precipitation towards the equator, this is why the equatorial regions receive more rainfall than the regions located away from the equator.

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37 is at the 50th percentile in the given set of values.

To find the percentile of 37 in the given set of values, we need to count the number of values in the set that are less than or equal to 37, and then divide by the total number of values in the set.

The given set has 16 values, and there are 8 values that are less than or equal to 37.

So, the percentile of 37 is:

Percentile = (number of values below score / total number of values) × 100

Percentile = (8 / 16) × 100

Percentile = 50

Therefore, 37 is at the 50th percentile in the given set of values.

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Answer:

The expected profit on the listing is $5031.96

Step-by-step explanation:

Given that:

The probability of selling the house in 6 months is p = 0.37

The probability of not selling the house = 1 - 0.37 = 0.63

Suppose Y represents the profit on the listing,

Then: the expected profit on the listing can be computed as:

E(X) = ($20283* 0.37) - ($3925*0.63)

E(X) = $7504.71 - $2472.75

E(X) = $5031.96

Thus, the expected profit on the listing is $5031.96

The expected profit on the listing is $5031.96.

Since

The probability of selling the house in 6 months is p = 0.37

The probability of not selling the house = 1 - 0.37 = 0.63

here Y means the profit on the listing,

So, the expected profit is

E(X) = ($20283* 0.37) - ($3925*0.63)

E(X) = $7504.71 - $2472.75

E(X) = $5031.96

Thus, the expected profit on the listing is $5031.96.

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The probability that the roots of the quadratic equation z^2 + 2Xz - 2X + 15 = 0 are real, where X is uniformly distributed in the interval (0, 4), is 0.25 or 1/4.

To find the probability that the roots of the quadratic equation z^2 + 2Xz - 2X + 15 = 0 are real, we can use the given hint, which states that the roots are real if b^2 - 4ac ≥ 0.

Comparing the quadratic equation to the standard form az^2 + bz + c = 0, we have:

a = 1, b = 2X, and c = -2X + 15.

Substituting these values into the inequality, we get:

(2X)^2 - 4(1)(-2X + 15) ≥ 0

4X^2 + 8X + 8X - 60 ≥ 0

4X^2 + 16X - 60 ≥ 0

X^2 + 4X - 15 ≥ 0

To find the values of X that satisfy this inequality, we can factorize the quadratic equation:

(X + 5)(X - 3) ≥ 0

The solutions to this inequality are X ≤ -5 or X ≥ 3. However, since X is uniformly distributed in the interval (0, 4), we need to consider the portion of the interval that satisfies X ≥ 3.

Therefore, the probability that the roots of the given quadratic equation are real is the probability of X being greater than or equal to 3, which is:

P(X ≥ 3) = (4 - 3) / (4 - 0) = 1/4 = 0.25.

Hence, the probability that the roots of the quadratic equation are real is 0.25.

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Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.

In the given figure the triangle ΔKFG and ΔFJH

KG is parallel to JH

Hence ΔKFG is similar to ΔFJH

Now using the property of similarity and proportion we can say that:

FG/FH = KF/JF

putting the values in the above proportion we get:

7 /(7+x) = 5/ 7

or, 49 = 35 +5 x

or, 14 = 5x

or, x =14/5

or, x = 2.8

The majority of ratio and percentage explanations involve using fractions.

A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.

Hence the value of x is 2.8 units.

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The number of coils (turns) in the toroidal solenoid of radius 6.00 cm and a cross-sectional area of 2.00 cm2 is approximately 1936.

Given:
The toroidal solenoid has an inductance (L) of 2.50 mH.
The average radius of the solenoid (r) is 6.00 cm.
The cross-sectional area (A) of the solenoid is 2.00 cm².

Formula to find inductance of toroidal solenoid:

L = μ₀ * μᵣ * N² * A / (2 * π * r)

L is the inductance of the toroidal solenoid.

μ₀ is the permeability of free space, which is 4π × 10^-7 T m A^-1.

μᵣ is the relative permeability of the core material.

N is the number of turns of wire around the toroid.

A is the cross-sectional area of the toroid. r is the average radius of the toroid.

π is the mathematical constant pi (approximately 3.14).

For the given inductance L, we can rearrange the formula as:

N = √(L * 2 * π * r / (μ₀ * μᵣ * A))

Now, substituting the values of L, r, and A, we get:

N = √(2.50 × 10^-3 * 2 * π * 6.00 × 10^-2 / (4π × 10^-7 * 1 * 2.00 × 10^-4))= √(3.75 × 10^5)≈ 1936.49 (approx.)

Hence, the number of coils (turns) in the toroidal solenoid is approximately 1936.

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The median of a sample will always equal the 50th percentile.

The median of sample data is the middle value when the data is arranged in order from lowest to highest. In other words, it is the value that separates the lower 50% of the data from the upper 50%.

The median is often used as a measure of central tendency in a dataset because it is not affected by extreme values or outliers in the way that the mean is. If the sample size is odd, the median is simply the middle value, If the sample size is even, the median is the average of the two middle values.

The median is also known as the second quartile and the 50th percentile. As a result, the median of a sample will always equal the 50th percentile.

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When AB and CD are cut by transversal, the angle ∠8 ≅ ∠6 as option A: vertical angles are congruent.

What is transversal?

In geometry, a transversal line intersects two lines in the same plane at two different locations. In the Euclidean plane, transversals help establish the parallelism of two or more other straight lines. It crosses two lines at separate locations. Transversal intersection results in numerous angles.

Two parallel line AB and CD is cut by a transversal.

Angles 1 to 8 are formed by the intersection of transversal with the parallel lines.

Mark needs to prove that ∠4 ≅ ∠6.

The table of proofs made by Mark is given.

The second steps states that ∠8 ≅ ∠6 therefore m ∠8 = m ∠6.

In the image it can be seen that ∠8 and ∠6 are opposite to each other and are also placed in a vertical position.

They form a vertically opposite angles pair.

And according to the properties of angles vertical pair of angles are congruent.

Therefore, Mark's step 2 is reasoned as vertical pair.

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Answer: in a quiet room or the library,

also you better summarize your geometry lessons and remember the formulas :P

Answer:

\(x = log(6) = 0.778\)

Step-by-step explanation:

\(6(10)^x - 3= 33\\6(10)^x=36\\10^x=6\\log(10^x) = log(6)\\x = log(6) = 0.778\)

Answer:

20%

Step-by-step explanation:

300 divide by 60. the answer is 20 percent

Answer:

4

Step-by-step explanation:

\( \frac{70 - 35.24}{8.69} \)

\( \frac{34.76}{8.69} \)

\( = 4\)

Answer:

X=17/8

Step-by-step explanation:

Answer:

48.5 and 34.5

Step-by-step explanation:

83 divided by 2 and then subtract 7

Answer:

45 and 38 equal 83 and 45 is 7 more than 38

Answer:

it is C

Step-by-step explanation:

got it right on edge

Answer:

1,582.6 in.3

Step-by-step explanation: