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1 year ago

Donovan took a math test and got 20 correct questions and 5 incorrect answers. What was the percentage of correct answers?

Mathematics

1 answer:

solong [7]1 year ago

3 0

ANSWER

80%

EXPLANATION

Donovan got 20 questions correct and 5 questions incorrect.

This means that the total number of questions he attempted in the test is the sum of correct and incorrect questions:

Total = 20 + 5

Total = 25

To find the percentage of correct answers, we have to divide the number of correct answers by the total number of questions attempted and multiply by 100 (per cent).

That is:

$\begin{gathered} \frac{20}{25}\cdot\text{ 100 = }\frac{4}{5}\cdot\text{ 100} \\ =\text{ 80\%} \end{gathered}$

That is the percentage of correct answers.

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What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

<u>Answer:</u>

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

<u>Solution: </u>

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

6 0

3 years ago

Can someone please help me with this :(

mrs_skeptik [129]

Answer:

first find the surface area of one of the square and one of the triangle.

then multiple it by the number of square and triangle they have

finally add the total surface area of the triangle with the total surface area of the square.

Step-by-step explanation:

for one square

area= base * width

= 10*10

=100

total area of square= number of square * area of one square

t=6*100

t=600

for one triangle

area = 1/2 base * height

= 1/2 *10*8.66

=43.3

total area of triangle=number of triangle* area of one triangle

t2=8*43.3

=346.4

total surface area= total surface area of the square+ total surface area of the triangle

=600+346.4

=946.4 in^2

5 0

3 years ago

A random sample of 102 full-grown lobsters had a mean weight of 16 ounces and a standard deviation of 3.4 ounces. Construct a 98

pshichka [43]

Answer:

The best point estimate for a confidence interval estimating the population μ is 16 ounces.

The 98 percent confidence interval for the population mean μ is between 15.21 ounces and 16.79 ounces.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The best point estimate for a confidence interval estimating the population μ is

The sample mean, so 16 ounces.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 102 - 1 = 101

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 101 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 2.36