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2 years ago

A body builder consumed 5,600 calories yesterday. Today, he consumed 4,200 calories.

Mathematics

1 answer:

hammer [34]2 years ago

5 0

well, the difference from 5600 to 4200 is 1400.

If we take 5600 to be the 100%, how much is 1400 off of it in percentage?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 5600&100\\ 1400&x \end{array}\implies \cfrac{5600}{1400}=\cfrac{100}{x}\implies 4=\cfrac{100}{x} \\\\\\ 4x=100\implies x=\cfrac{100}{4}\implies x=25$

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If cos theta=-3/5 in quadrant 2 what is sin theta? A:4/5 B:3/4 C:-3/4 D:-4/5

Scrat [10]

Answer: Choice A) 4/5

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

Work Shown:

cos^2(theta) + sin^2(theta) = 1
(-3/5)^2 + sin^2(theta) = 1
9/25 + sin^2(theta) = 1
9/25 + sin^2(theta) - 9/25 = 1 - 9/25
sin^2(theta) = 1 - 9/25
sin^2(theta) = 25/25 - 9/25
sin^2(theta) = (25 - 9)/25
sin^2(theta) = 16/25
sqrt[sin^2(theta)] = sqrt[16/25]
sin(theta) = 4/5

The fact that sine is positive in quadrant 2 means that the result is positive.

8 0

2 years ago

If X = 2 centimeters, Y = 5 centimeters, and Z = 5 centimeters, what is the area of the object?

Elena L [17]

Answer: $35 cm^2$

Step-by-step explanation:

Area of trapezium =

2X = 2 + 2 = 4 cm

2Z = 5 + 5 = 10 cm

Y = 5 cm

$\dfrac{ \left( 4+10 \right) }{ 2 } \times 5$

|--------> 35 $cm^2$

6 0

1 year ago

Find the slope and y-intercept of the graph of 4x-3=36

Oxana [17]

Answer: Slope is undefined or aka infinity, and there is no y-intercept

Step-by-step explanation:

Using Slope-Intercept Form to find the slope and the y-intercept.

First, lets change 4x-3=36 into y=mx+b. When you change it into this form you'll see that it can't go into intercept form because x=39/4 and is a vertical line so the slope is undefined or aka infinity, and there is no y-intercept.

Hope this helps! Have a nice day! ❤

- Cutiepatutie

6 0

3 years ago

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

10 months ago

Evaluate the integral by interpreting it in terms of areas Draw a picture of the region the integral

denis23 [38]

Answer:

Step-by-step explanation:

The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.

For the integral from [0, 2], the equation of the line is -3x + 6;

For the integral from [2, 3], the equation of the line is 3x - 6.

We integrate then:

$\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx$ and

$-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right. +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.$ sorry for the odd representation; that's as good as it gets here!

Using the First Fundamental Theorem of Calculus, we get:

(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5

5 0

2 years ago