4 points: A,B,C and D are marked in order on a line such that AB:AC = 3:7 and BD:CD= 9:2. If CD is 100cm long, find the length of AB.

Final answer:

The expression 2d(3) is simplified by multiplying 2 by 3, yielding 6, and then by d, resulting in 6d.

Explanation:

To simplify the expression 2d(3), you simply need to multiply the variable d by the number 2 and then multiply the result by the number inside the parentheses, which is 3. This is straightforward multiplication, similar to the distributive property used in algebra to simplify expressions.

The simplified form of the expression is found by multiplying 2 by 3, giving us 6, and then multiplying that result by d. Hence, 2d(3) simplifies to 6d.

Answer: 250 coins

Step-by-step explanation:

Betsy has 25 quarters

let quarters = q

nickels = n

pennies  =  p

n = 3q = 3*25 = 75

p = 2n = 2* 75 = 150

she has total  of 25 + 75 + 150= 250 coins

General Idea:

Pythagorean theorem states that in a right triangle, if side of triangle is given by ' a ', bottom of the triangle is given by ' b ' and hypotenuse of triangle is given by ' c', then Sum of squares of a and b is equal to the square of hypotenuse.

[tex] a^{2} \; +\; b^{2}\; =\; c^{2} [/tex]

Applying the Concept:

[tex] Given\\Side\;of\;triangle\;(a)\; =\; 8\\ Bottom\;of\;triangle\;(b)=15\\ \\ To\; Find\\Hyptotenuse\;(c)\\ \\ a^{2}+b^{2}=c^{2}\\ 8^2+15^2=c^2\\ \\ 64+225=c^2\\ \\ 289=c^2\\ \\ c^2=289\\ Taking \; Square\;root\;on\;both\;sides\\ \\ \sqrt{c^2}=\sqrt{289} \\ \\ c=17 [/tex]

Conclusion:

The length of the missing side of the right triangle, when side 8 & bottom 15 is 17. The correct answer is option B!!

Answer:

B. $2492.36

Step-by-step explanation:

We are given the formula for compound interest,

[tex]A(t)=p(1+i)^x[/tex] where p is the amount of principal, i is the interest rate and x is the number of years.

In our problem, p is 2000, i = 4.5% = 4.5/100 = 0.045, and x is 5:

[tex]A(t)=2000(1+0.045)^x\\\\A(5)=2000(1.045)^5\approx 2492.36[/tex]

Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.

Compound interest is the interest which is received on the principal and the previous interest.

Amount [tex]=P(1+\frac{R}{100})^t[/tex]

We have,

Invested principal [tex]=\$2000[/tex]

Compound interest Rate [tex]=4.5\%[/tex]

Time of investment [tex]=5[/tex] years

So,

Using the above mentioned formula;

Amount [tex]=P(1+\frac{R}{100})^t[/tex]

              [tex]=2000(1+\frac{4.5}{100})^5[/tex]

              [tex]=2000(1+\frac{9}{200})^5[/tex]

              [tex]=2000\ *\ (\frac{209}{200})^5[/tex]

Amount [tex]=\$\ 2492.36[/tex]

So, Amount in Maria's account is [tex]\$\ 2492.36[/tex].

Hence, we can say that Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.

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Answer:

4/8

Step-by-step explanation:

Final answer:

A computer that uses 4W of power during 'vampire' mode over weekends throughout a year produces approximately 4.992 kg of CO2 annually. This is calculated by multiplying the total hours in vampire mode by the power consumption and then by the CO2 emission factor for electricity.

Explanation:

To calculate the amount of carbon dioxide produced from the vampire energy used by a computer that is not unplugged, we first have to establish the power consumption while in 'vampire' mode. The power consumed by the computer's LED when it is turned off but not unplugged is stated to be about 4 watts (W).

A year has 52 weeks, and each weekend amounts to 60 hours of the computer being in 'vampire' mode. To find the total number of hours in a year this mode occurs, we multiply 60 hours by 52, which gives us 3,120 hours of energy consumption annually when the computer is in 'standby' mode.

Next, to convert the total power consumed in watts to kilowatt-hours (kWh), we divide the power in watts by 1,000 (since 1 kW = 1,000 W), and then multiply by the total hours per year.

The carbon dioxide emissions can be estimated using an average emission factor for electricity production. For example, if we assume that the emission factor is about 0.4 kilograms of CO2 per kWh (which varies based on local energy sources), we can calculate the total emissions for the computer's vampire energy consumption.

Calculations: 4 W ÷ 1,000 = 0.004 kW
0.004 kW × 3,120 hours/year = 12.48 kWh/year
12.48 kWh/year × 0.4 kg CO2/kWh = 4.992 kg CO2/year

Therefore, the computer produces approximately 4.992 kg of CO2 annually from vampire energy when not unplugged over weekends.

Here are a bunch of CORRECT answers. Your answer is in the first pic. I got number 3 wrong, but it still showed the correct answer.

After rotating angle Q, which initially measures 30 degrees, by 15 degrees, the new angle Q' measures 45 degrees.

When we talk about rotating an angle, we are referring to moving the angle around its vertex through a specified measure. If we have angle Q which measures 30 degrees and we rotate it by 15 degrees, we are effectively adding 15 degrees to the original angle. Thus, the measure of angle Q' will be 30 degrees plus 15 degrees which equals 45 degrees. Rotations do not change the original angle but instead give us a new angle based on the original position plus the rotation.

The equation 3sec (x) -2 = 1 solved on the interval is x = 0

From the question, we have the following parameters that can be used in our computation:

3sec (x) -2 = 1

Express sec(x) as 1/cos(x)

So, we have

3 * (1 / cos (x)) - 2 = 1

Add 2 to both sides

3 * (1 / cos (x)) = 1 + 2

Evaluate the like terms

3 (1 / cos (x)) = 3

Divide through by 3

(1 / cos (x)) = 3/3

So, we have

cos (x) =  1

Take the arc cos of both sides

x = 2nπ

On the interval [0, 2π), we have x = 0

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The sales tax rate was calculated based on the information of the first item, and we found it to be approximately 8.09%. Using this tax rate, the pre-tax price of the second item, on which the sales tax was $19.25, was found to be approximately $237.85.

To solve this problem, we first need to determine the percentage rate of the sales tax based on the first item. Given that a sales tax of $22 was applied to an item that cost $272 before tax, we can calculate the tax rate as follows: (22/272)*100 = 8.09%. This indicates that the tax rate is approximately 8.09%.

Next, if we assume that the sales tax rate is the same for the second item, we can calculate the pre-tax price of this item. Given that the sales tax on the second item is $19.25, the price of the item before tax can be calculated as follows: 19.25/0.0809 = $237.85 approximately. Therefore, the second item costs about $237.85 before tax.

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The tree is 15 feet tall

The tree in Pedro's front yard was 5 ft tall last year.

This year, the tree is 2 feet less than the height of Pedro's house.

let

the height of the tree = x

Therefore,

height of the house = 17 feet

17 - 2 = x

x = 15 ft

Therefore, the tree is 15 feet tall

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The tree in Pedro's front yard is currently 15 feet tall, which is 2 feet shorter than the height of Pedro's 17 feet tall house.

Last year, the tree in Pedro's front yard was 5 feet tall. This year, the tree is 2 feet shorter than the height of Pedro's house. If Pedro's house is 17 feet tall, we need to calculate the tree's current height by subtracting 2 feet from the height of the house. Therefore, the tree's current height would be 17 feet - 2 feet = 15 feet tall.