Answer:
The area of the triangle is of 21 units of area.
Step-by-step explanation:
The area of a triangle with three vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] is given by the determinant of the following matrix:
[tex]A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|[/tex]
In this question:
Vertices (3,0) (9,0) (7,6). So
[tex]A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|[/tex]
[tex]A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)[/tex]
[tex]A = \pm 0.5*(63-21)[/tex]
[tex]A = \pm 0.5*42 = 21[/tex]
The area of the triangle is of 21 units of area.
Can anyone help me? I am stuck on this question! it would mean the world if u helped me! <3
Answer:
I think the answer is 12
Step-by-step explanation:
Is this correct? Can someone please help me!!
What is the total surface area of the rectangular pyramid below?
Answer:
c. SA = 596 ft²
Step-by-step explanation:
Area of the rectangular pyramid = Base area + area of the 2 equal lateral faces + area of the 2 lateral faces
Base area = length × width
Length = 16 ft
Width = 12 ft
Base area = 16 × 12 = 192 ft²
Area of the 2 lateral faces with the following dimension:
base = 12 ft
height = 15 ft
Area = 2(½bh) = 2(½*12*15) = 180 ft²
Area of the 2 lateral faces with the following dimensions:
base = 16 ft
height = 14 ft
Area = 2(½*14*16) = 224 ft²
✅Total surface area = 192 + 180 + 224 = 596 ft²
Emma placed 100 golf balls in a bag. Thirty six of the golf balls were red 24 were blue and the rest were green . If Emma drew one golf ball from the bag without looking what is the probability that the golf ball was red
Answer:
0.36
Step-by-step explanation:
R=36
B=24
total=100
probability that its red =36/100
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 35 arrests last month, 27 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.7; H1: p ≠ 0.7
H0: p = 0 .7; H1: p < 0.7
H0: p < 0 .7; H1: p = 0.7
H0: p = 0.7; H1: p > 0.7
H0: p ≠ 0.7; H1: p = 0.7
(b) What sampling distribution will you use?
The Student's t, since np < 5 and nq < 5.
The standard normal, since np < 5 and nq < 5.
The standard normal, since np > 5 and nq > 5.
The Student's t, since np > 5 and nq > 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.
At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.
There is insufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.
Answer:
a) Level of significance [tex]\alpha = 0.01[/tex]
b) Standard normal
[tex]p = 0.75[/tex]
[tex]Z = 0.62[/tex]
c)
[tex]P = 0.5352[/tex]
d)
[tex]P > \alpha[/tex]
e) We fail to reject null hypothesis
Step-by-step explanation:
Let us say
The null hypothesis H_0 is p= 0.70 which means that Probability of arresting male of age ranging between 15 to 34 years is 0.7
Alternate hypothesis H_1 is p not equal to 0.7 which means that Probability of arresting male of age ranging between 15 to 34 years is not equal to 0.7
a) For 1% level of significance [tex]\alpha = 0.01[/tex]
b) Standard normal
[tex]n_p > 5\\n_q >5[/tex]
[tex]p = \frac{24}{32} = 0.75[/tex]
[tex]Z = \frac{(0.75-0.70)}{\sqrt{\frac{(0.7*0.3)}{32} } } = 0.62[/tex]
c)
[tex]P = 2 * 0.2676 = 0.5352[/tex]
d)
[tex]P > \alpha[/tex]
e) We fail to reject null hypothesis
Hence, there is not enough data to prove that at 1% level of significance the probability of number of male arrested between age 15-34 is 0.70
What is the product of the expressions (3)(−2)(−5)(7)?
Answer:
210
Step-by-step explanation:
3*10*7
30*7
210
Remember when multiplying even number of negative terms, it cancels out the negative.
Find the length of side XZ 12.6cm 29°
Answer:
XZ ≈ 14.4 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos29° = = =
Multiply both sides by XZ
XZ × cos29° = 12.6 ( divide both sides by cos29° )
XZ = ≈ 14. 4 ( to 3 sig. figs )
Answer:
14.4
Step-by-step explanation:
What’s the derivative of x^2 - 3
Answer:
[tex]\displaystyle \frac{dy}{dx} = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2 - 3[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[x^2] - \frac{d}{dx}[3][/tex]Basic Power Rule: [tex]\displaystyle y' = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
1. A cardboard box is 5 feet long, 1.5 feet
wide, and 2 feet high. Which of the
following answers is closest to the
volume of the box in cubic feet?
A. 8.5 ft.3
B. 15 ft.3
C. 18 ft.3
D. 24 ft.3
Answer:
The correct answer is B.
Step-by-step explanation:
V=whl=1.5·2·5=15
Answer:
B. 15 ft.3
Step-by-step explanation:
multiply all the measurements to find the volume :)
f(x)=3x2+1
What is the value of y when x is equal to 0?
Hint: f(0)=3(0)2+1
What is the solution to the equation?
a+5 2/3=9
PLEASE HELP!!!!
Answer:
a = -25
Step-by-step explanation: a+ 52/3 =9
multiply both sides by 3
3(a+52)/3 = 9.3
Simplify
a+52=27
Subtract 52 from both sides
a+52-52=27-52
Simplify
a= -25
Which equation has roots -3 and 4
Answer:
x^2 - x - 12 (this is the second answer choice)
Step-by-step explanation:
Multiply (x + 3)(x - 4) and simplify the result:
x^2 - 4x + 3x - 12, or x^2 - x - 12 (this is the second answer choice)
Given sin r = 0.5, what is cos r?
enter your answer as a decimal, rounded to the nearest hundredth.
Answer:
0.877 but rounded it will be 0.88
Factorise the following:
a² - 144
Answer:
[tex]( a+ 12)(a - 12)[/tex]
Step-by-step explanation:
[tex] {a}^{2} - 144[/tex]
[tex] {a}^{2} - {12}^{2} [/tex]
Since both terms are perfect squares, factor using the difference of squares formula,
[tex] {a}^{2} - {b}^{2} = ( a+b )(a - b)[/tex]
where a=a and b=12.
[tex](a+ 12)(a - 12)[/tex]
Hope it is helpful....25. Angie inherits a collection of 4213 antique duck-calls from her grandmother. If she goes around to yard sales and adds another 3 duck-calls to the collection every weekend, what's an equation that models her total collection?
A) y = 3x
B) y= 3x - 4213
C) y= 3x + 4213
D) y = 4213x+ 3
Answer:
C
Step-by-step explanation:
Angie already has a fixed number of antiques - 4213 antiques. the rate of increase of ducks would depend on the number of weekends. this is the variable number of antiques
thus the equation is :
y = 4213 + 3x
What is the volume of the sphere shown below?
13
image below
Create a Pythagorean theorem equation for the diagram then solve the unknown sides. If necessary, rounded to decimal places.
The value of the unknown side using the Pythagorean theorem to two decimal places is 5.39.
What is the value of the unkown side?
The Pythagorean theorem would be used to solve for the unknown side.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse√5² + 2²
√25 + 4
√29 = 5.39
To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675
Could you guys help me?
Answer:
its 1881
Step-by-step explanation:
banakz akaknsz a a
Find the value of 1
and 1/10-1/5
9514 1404 393
Answer:
9/10
Step-by-step explanation:
(1 1/10) - 1/5 = (1 1/10) -2/10 = 1 + (1/10 -2/10) = 1 -1/10 = 9/10
__
1.1 -0.2 = 0.9 = 9/10
Is 2/10 smaller than 19/100?
Answer:
Step-by-step explanation:
no cause 2/10 is the same as 20/100
if pablo does a experiment 100 times, will the relative frequency be more accurate or less accurate than if he did the experiment 40 times
Why?
Answer:
As the number of trials increases, the relative frequency becomes closer to the probability of the event. So, the relative frequency would be more accurate if the experiment were repeated 100 times rather than 40 times.
Step-by-step explanation:
This is the sample for edmentum so you might to change it up a bit! Hope this help. <33
HELP!!!!!!!!!!
A student divided f(x) = 3x^3 + 8x^2 + 5x – 4 by x + 2 and found the remainder was r = -6. Based
on the remainder theorem, what can be concluded about f(x)?
Answer:a
Step-by-step explanation:
The point (-2, -6) lies on the graph of a function f(x) if the f(x) = 3x^3 + 8x^2 + 5x – 4 divided by x + 2 and found the remainder was r = -6 option fourth is correct.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
Let's suppose the divisor is Q
Then from the remainder theorem:
f(x) = (x+2)Q -6
[tex]\rm 3x^3+8x^2+5x-4=(x+2)Q-6[/tex]
If we put x = -2, then
[tex]\rm 3(-2)^3+8(-2)^2+5(-2)-4=(-2+2)Q-6[/tex]
[tex]\rm 3\times-8+8\times4-10-4=-6[/tex]
-24 + 32 -10 -4 = -6
-6 = -6
It means (-2, -6) lies on the function(also refer the graph of the function)
Thus, the point (-2, -6) lies on the graph of a function f(x) if the f(x) = 3x^3 + 8x^2 + 5x – 4 divided by x + 2 and found the remainder was r = -6 option fourth is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ2
Which One Doesn’t Belong?
7.9x
7.9 (-10)
7.9 + x
-79
Answer:
in the 1 one of you choice
Step-by-step explanation:
Help me this question is very confusing no wrong answers please
Answer:
10
Step-by-step explanation:
maximum= most walked
then minimum would be least amount walked
Answer:
Answer = 10
Step-by-step explanation:
Mark me as Brainliest
SOMEONE PLZ HELP A$AP
Answer:
<
Step-by-step explanation:
I used a scientific calculator, 2² is 4 and when I take 4.7 × 10-³ minus 4 the answer is negative, so I'm guessing that it's a number less than 4.
Again, I haven't learned this yet since I'm 12 so it might be wrong.
If (-1, y) lies on the graph of y = 2²x, then y =
Answer: look at the picture
Step-by-step explanation: Hope this help :D
What is the diameter of a hemisphere with a volume of 877 m^3 to the nearest tenth of a meter?
Answer:
15.0
Step-by-step explanation:
It’s on deltamath
An investment of 8,500 has an annual interest rate of 6.6%...... (Continues in screenshot) (please explain)
Answer:
C) A = 8500(1.0165)^16
Step-by-step explanation:
A = P(1 + r/n)^nt where 'n' is # times compounded and 't' is time in years
A = 8500(1 + (.066/4))^4·4
A = 8500(1 + 0.0165)^16
The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $8,000. Sixteen teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500?
Answer:
0.1056 = 10.56% probability that their average salary is more than $77,500.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean $75,000 and standard deviation $8,000.
This means that [tex]\mu = 75000, \sigma = 8000[/tex]
Sample of 16
This means that [tex]n = 16, s = \frac{8000}{\sqrt{16}} = 2000[/tex]
What is the probability that their average salary is more than $77,500?
This is 1 subtracted by the pvalue of Z when X = 77500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{77500 - 75000}{2000}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.1056 = 10.56% probability that their average salary is more than $77,500.
In a geometric sequence, a2 = 2, a3 = 20, & a4 = 200.
Which equation can be used to find the nth term of the sequence, an?
an = 10 * 2n-1
an = 2n-1
an = 1/5 * 10n-1
an = 2 * 18n-1
Answer:
the first one
the first one Step-by-step explanation:
the first one Step-by-step explanation:from the formula Un =ar^n-1
where a is 2
where a is 2 r = 20/2=10
where a is 2 r = 20/2=10 so Un= 10×2^n-1
that's all.....have fun
Answer:
C.) an =1/5 * 10n-1
Step-by-step explanation:
D.) is out of the question just at first look.
A.) is irregular to the sequence, giving you the wrong outputs.
B.) is also irregular to the sequence.
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