MATHEMATICS COLLEGE

What is the length of the unknown side of the right triangle?

Answers

Answer 1

Answer:

Hypotenuse

Step-by-step explanation:

Answer 2

Answer:

Answer:

L= the sum of the square root of the square of the opposite side and the square of the base the triangle.

Step-by-step explanation:

Using Pythagorean Theorem :

the square of the hypotenuse= the square of the opposite side + the square of the base.

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For each pair of lines, determine whether they are parallel, perpendicular, or neither Line1 : 2y=5x+7 Line2: 4x+10y=8Line3: y=5/2x-4
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(- 5x + 5) + (- 7x + 9) = 90 degrees

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

Answers

The answer is 38 peas per pod

228÷6 = 38

Glad to help you :)

Final answer:

By dividing the total number of peas (228) by the number of peas per pod (6), we find that Gregor Mendel has 38 pods of peas.

Explanation:

This question is asking how many pods of peas Gregor Mendel has if he has a total of 228 peas and each pod contains 6 peas. To find out this, you can divide the total number of peas by the number of peas per pod.

So, 228 peas ÷ 6 peas/pod = 38 pods.

Therefore, Gregor Mendel has 38 pods of peas that he is examining for his research.

Learn more about Division here:

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what is 10*2*8-3(8*5)

Answers

Let's break it down quick

since (8*5) is in parenthesis, you have to do it first which would equal 40. 10*2=20*8 is 160. Since there is a negative in between that and 3*40 you must solve 3*40 first, which equals 120. Now,

160-120= 40

The answer to the question is 40.

Hey and thanks for giving me the chance to serve u

10*2=20*8 is 160. then this

160-120= 40
So we get 40(:

Hope l helped

If f(x)=8x then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=6

Answers

Answer:

$A=128$

Step-by-step explanation:

First of all we need to graph f(x)=8x, (First picture)

Now we have to calculate the area enclosed by the graph of the function, the horizontal axis, and vertical lines at $x_(1)=2$ and $x_(2)=6$ ,

The area that we have to calculate is in pink (second picture).

The function is positive and the domain is $[2,6]$ then we can calculate the area with this formula:

$A=\int\limits^b_a {f(x)} \, dx$ ,

In this case $b=x_(2) , a=x_(1)$

$A=\int\limits^6_2 {8x} \, dx = 8\int\limits^6_2 {x} \, dx$

The result of the integral is,

$A=8(x^(2))/(2)$ , but the integral is defined in [2,6] so we have to apply Barrow's rule,

Barrow's rule:

If f is continuous in [a,b] and F is a primitive of f in [a,b], then:

$\int\limits^b_a {f(x)} \, dx =F(b)-F(a)$

Applying Barrow's rule the result is:

$A=8.(6^(2) )/(2)-8.(2^(2) )/(2)$

$A=8.(36)/(2) -8.(4)/(2)$

$A=144-16$

$A=128$

ree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 119 inches and standard deviation σ = 17 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least four decimal places. (a) What proportion of trees are more than 130 inches tall? (b) What proportion of trees are less than 90 inches tall? (c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall? Part: 0 / 30 of 3 Parts Complete Part 1 of 3 What proportion of trees are more than 130 inches tall? The proportion of trees that are more than 130 inches tall is .

Answers

Answer:

a) 0.2588

b) 0.044015

c) 0.12609

Step-by-step explanation:

Using the TI-84 PLUS calculator

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question, we know that:

μ = 119 inches

standard deviation σ = 17 inches

(a) What proportion of trees are more than 130 inches tall?

x = 130 inches

z = (130-119)/17

= 0.64706

Probabilty value from Z-Table:

P(x<130) = 0.7412

P(x>130) = 1 - P(x<130) = 0.2588

(b) What proportion of trees are less than 90 inches tall?

x = 90 inches

z = (90-119)/17

=-1.70588

Probability value from Z-Table:

P(x<90) = 0.044015

For x = 95

z = (95-119)/17

= -1.41176

Probability value from Z-Table:

P(x = 95) = 0.07901

For x = 105

z = (105 -119)/17

=-0.82353

Probability value from Z-Table:

P(x<105) = 0.2051

The probability that a randomly chosen tree is between 95 and 105 inches tall

P(x = 105) - P(x = 95)

0.2051 - 0.07901

= 0.12609

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 6 sin x, y = 6 cos x, 0 ≤ x ≤ π/4; about y = −1

Answers

hmm well, here an example y=3 ,

y=3 , rather than the x− x− axis.) Your integrand looks fine and reduces to

(9−18sinx+9sin2x) − (9−18cosx+9cos2x) (9−18sin⁡x+9sin2⁡x) − (9−18cos⁡x+9cos2⁡x)

= 18 (cosx−sinx) + 9 (sin2x−cos2x) = 18 (cosx−sinx) − 9 cos2x .= 18 (cos⁡x−sin⁡x) + 9 (sin2⁡x−cos2⁡x) = 18 (cos⁡x−sin⁡x) − 9 cos⁡2x .

The evaluation of the volume is then

π [ 18 (sinx+cosx) − 92sin2x ]π/40π [ 18 (sin⁡x+cos⁡x) − 92sin⁡2x ]0π/4

= π ( [ 18 ( 2–√2+2–√2) − 92⋅1 ] − [ 18 (0+1) − 92⋅0 ] ) = π ( [ 18 ( 22+22) − 92⋅1 ] − [ 18 (0+1) − 92⋅0 ] )

= π ( 182–√ − 92 − 18 ) = π ( 182–√ − 452 ) or 9π2 ( 42–√ − 5 ) ,

Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Answers

Answer:

The answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

Step-by-step explanation:

$\bold{\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]}$

Solve the L.H.S part:

$\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right]\n\n\n\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]$

After calculating the L.H.S part compare the value with R.H.S:

$\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]} \n\n$

$\to a+2c =6....(i)\n\n\to b+2d =5....(ii)\n\n\to 3a+4c =19....(iii)\n\n\to 3b+4d = 8 ....(iv)\n\n$

In equation (i) multiply by 3 and subtract by equation (iii):

$\to 3a+6c=18\n\to 3a+4c=19\n\n\text{subtract}... \n\n\to 2c = -1\n\n\to c= - (1)/(2)$

put the value of c in equation (i):

$\to a+ 2 (- (1)/(2))=6\n\n\to a- 2 * (1)/(2)=6\n\n\to a- 1=6\n\n\to a =6 +1\n\n\to a = 7\n$

In equation (ii) multiply by 3 then subtract by equation (iv):

$\to 3b+6d=15\n\to 3b+4d=8\n\n\text{subtract...}\n\n\to 2d = 7\n\n\to d= (7)/(2)\n$

put the value of d in equation (iv):

$\to 3b+4 ((7)/(2))=8\n\n\to 3b+4 * (7)/(2)=8\n\n\to 3b+14=8\n\n\to 3b =8-14\n\n\to 3b = -6\n\n\to b= (-6)/(3)\n\n\to b= -2$

The final answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

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The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. Is the following a Type I error or a Type II error or neither? The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is. Group of answer choices Type I error Type II error

Please help me! Determine the area

The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time.

True or false Every number divisible by 9 is also by 3?