Answer:
15 units
Step-by-step explanation:
1. Find the corresponding lengths of the triangles.
9/x = x/ (9+16)
9/x = x/25
2. Solve for x.
Multiply both sides by x.
9 = x²/25
Multiply both sides by 25.
225 = x²
Square root both sides to solve for x.
√225 = √x²
x = 15
The display on a calculator screen is shown2.119188EE-8. What number does the calculator represent
Answer:
0.00000002119188
Step-by-step explanation:
If you enter this number into a spreadsheet (with a single E), you can set the display format to show you the value in standard form. The exponent (E) of -8 indicates the most-significant digit (2) is in the 8th place to the right of the decimal point:
= 2.119188×10^-8
= 0.00000002119188
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
7th grade math I need help with this
Answer:
each bag of candy is $6.00
Step-by-step explanation:
1 bag would cost $6.00
1×$6.00=$6.00
6 bags × $6.00 = $36.00
Answer:
the constant of proportionally is 6
the prices of 6 bags of candy is 36
Step-by-step explanation:
to find the constant u divide 6 by 1 to find how they multiplying it by
the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36
hope this helps
Please help ASAP
April runs at a rate of 25 feet per second for 11 seconds. Determine how far she
traveled and select the appropriate units to describe it.
She traveled ___________
Isaac drove on the interstate for 3 hours and traveled a total of 165 miles.
Determine his rate of travel and select the appropriate units to describe it.
He traveled ___________
Answer:
1. distance = 275 ft
2. rate = 55 miles/hour
Step-by-step explanation:
April travels at the rate of 25 ft per seconds and the time she spent traveling is 11 seconds. How far she traveled is the distance she covered. The rate or the speed unit is given as ft per seconds. Therefore, the distance covered can be expressed as follows.
rate = distance/time
where
rate = 25 ft/sec
time = 11 secs
rate = distance/time
25 = distance/11
cross multiply
distance = 25 × 11
distance = 275 ft
Isaac drove for 3 hours and he covered a distance of 165 miles. The rate of travel can be expressed as follows
rate = distance/time
distance = 165 miles
time = 3 hours
rate = 165/3
rate = 55 miles/hour
Select whether the equation has a solution or not.
[tex] \sqrt{4x + 5} - \sqrt{x - 1} = \sqrt{x + 4} [/tex]
Answer:
5 is solution
Step-by-step explanation:
hello,
I am not sure what is expected for this kind of question.
we can notice that 5 is a solution as
[tex]\sqrt{4*5+5}-\sqrt{5-1}=\sqrt{25}-\sqrt{4}=5-2=3\\and\\\sqrt{5+4}=\sqrt{9}=3[/tex]
hope this helps
Please answer this correctly
Answer:
no
Step-by-step explanation:
No, it is not a random sample of the students in school.
Answer:
No
Step-by-step explanation:
A random sample is a sample that is taken from a larger set. Molly specifically chose to interview the youngest students, so the sample is not random.
Complete the recursive formula of the geometric sequence 10,6, 3.6, 2.16
Answer:
a(1) = 10
a(n) = a(n-1)·0.6
Step-by-step explanation:
The first term of the sequence is the one listed first: 10. That means a(1) = 10.
The next term of the geometric sequence will be the first term multiplied by the common ratio. That ratio can be found as the ratio of the second term to the first:
r = 6/10 = 0.6
So, the recursive formula is ...
a(n) = a(n-1)·r
a(n) = a(n-1)·0.6
Answer:
a(1) = 10
a(n) = a(n-1)·0.6
Describe a Type I error for this test.
A. Concluding that the average level of mercury uptake in wading birds in a region today is equal to 16 parts per million, when in fact, the average level of mercury uptake in wading birds in a region today is lessless than 16 parts per million.
B. Concluding that the average level of mercury uptake in wading birds in a region today is moremore than 16 parts per million, when in fact, the average level of mercury uptake in wading birds in a region today is equal to 16 parts per million.
C. Concluding that the average level of mercury uptake in wading birds in a region today is lessless than 16 parts per million, when in fact, the average level of mercury uptake in wading birds in a region today is equal to 16 parts per million.
Answer:
The correct option is (C).
Step-by-step explanation:
Missing information:
According to a university of wildlife ecology and conservation researcher, the average level of mercury uptake in wading birds in a region has declined over the past several years. Five years ago, the average level was 16 parts per million. Give the null and alternative hypotheses for testing whether the average level today is less than 16 ppm.
The hypothesis can be defined as follows:
H₀: The average level of mercury uptake in wading birds in a region is 16 ppm, i.e. μ = 16.
Hₐ: The average level of mercury uptake in wading birds in a region is less than 16 ppm, i.e. μ < 16.
A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.
In this case the type I error can be defined as:
Concluding that the average level of mercury uptake in wading birds in a region today is less than 16 parts per million, when in fact, the average level of mercury uptake in wading birds in a region today is equal to 16 parts per million.
The correct option is (C).
Someone please help ASAP
Answer:
[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]
Step-by-step explanation:
hello,
saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]
means that 1 is a root of this expression, so it comes
1+1-1-k=0
<=> 1-k=0
<=> k = 1
A nighttime cold medicine’s label indicates the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selects 65 1-ounce samples and finds the mean content is 595 mg with a standard deviation of 20 mg. Is there evidence that the label is incorrect? Use a= .05.
Answer:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
Step-by-step explanation:
Information given
[tex]\bar X=595[/tex] represent the sample mean
[tex]s=20[/tex] represent the sample standard deviation
[tex]n=65[/tex] sample size
[tex]\mu_o =600[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is different from 600 mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 600[/tex]
Alternative hypothesis:[tex]\mu \neq 600[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
represent 5 20 30 25 10 on a pie chart
Answer :
I have solved for the points.
Explanation :
Just get a protractor and plot out the angles into a circle. Starting with the largest angle.
Multiple(x-4)(2x+3) using the distributive property
Answer:
See Below
Step-by-step explanation:
x(2x) - 4(2x) + x(3) - 4(3)
= 2x² - 8x + 3x -12
= 2x²-5x-12
Jessica is walking home from a friend's house. After two minutes she is 0.8 miles from home. Twelve minutes after leaving, she is 0.3 miles from home. What is her rate in miles per hour
Answer:
3 miles per hour
Step-by-step explanation:
Jessica is walking home from a friend's house.
After 2 minutes she is 0.8 miles from the home and after 12 minutes she is 0.3 miles away fro her house.
Her rate will be = (change in distance)/change in time
= (0.8-0.3)/(12-2)
= 0.5/10
= 0.05 miles per minute
Now we will convert timings from minutes to hour.
Or = 0.05×60
= 3 miles per hour
AC is tangent to circle O at point C. What is the measure of angle ACO?
Answer:
m < ACO = 90 degrees.
Step-by-step explanation:
The line joining the center O of the circle to the point of contact of the tangent is a right angle.
Answer: 90 degrees
Step-by-step explanation: Khan academy
Need help please :) thanks
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
[tex]x=2$\pm$\sqrt{42}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]
Formula:
A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:
[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]
Where [tex]D= b^{2} -4ac[/tex]
Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]
a = 1
b = -4
c= -38
Calculating D,
[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]
Now, finding the roots:
[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]
So, the solution is:
[tex]x=2$\pm$\sqrt{42}[/tex]
Answer is A or the first one
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
A stock lost 7 1/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stock for these three days?
Answer:
It was gained 4 1/4 points.
Step-by-step explanation:
- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 = 4 1/4
Given: A, B, and C What is the value of X in the matrix equation AX + B = C?
Answer:
Option (2)
Step-by-step explanation:
Given expression is, AX + B = C
[tex]A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}[/tex]
AX + B = C
AX = C - B
C - B = [tex]\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}[/tex] = [tex]\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}[/tex]
C - B = [tex]\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}[/tex]
Let [tex]X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex]
AX = [tex]\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}[/tex]
Since AX = C - B
[tex]\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}[/tex]
Therefore, a = 1, b = 5
(-3a - 4c) = -35
3(1) + 4c = 35
3 + 4c = 35
4c = 32
c = 8
And (-3b - 4d) = -11
3(5) + 4d = 11
4d = -4
d = -1
Therefore, Option (2). X = [tex]\begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix}[/tex] will be the answer.
Answer:
the second option is your answer
Step-by-step explanation:
In rhombus MNOP, mMNO = 24. What is the measure of PMO
PLEASE answer pic provided
Answer:
Graphing Linear Inequalities
This is a graph of a linear inequality:
linear inequality y <= x +2
The inequality y ≤ x + 2
You can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2
Linear Inequality
A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...
... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.
How to Graph a Linear Inequality
First, graph the "equals" line, then shade in the correct area.
There are three steps:
Rearrange the equation so "y" is on the left and everything else on the right.
Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).
Let us try some examples:
Example: y≤2x-1
1. The inequality already has "y" on the left and everything else on the right, so no need to rearrange
2. Plot y=2x-1 (as a solid line because y≤ includes equal to)
Find the value of x for which line a is parallel to line b. 34 32 68 56
Answer
value of x is 34 degrees
Step-by-step explanation:
A lumber company is making boards that are 2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 21 is made, and it is found that they have a mean of 2567.0 millimeters with a variance of 121.00. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Step-by-step explanation:
Information given
[tex]\bar X=2567[/tex] represent the mean height for the sample
[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation
[tex]n=21[/tex] sample size
[tex]\mu_o =2564[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2564[/tex]
Alternative hypothesis:[tex]\mu \neq 2564[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
As part of a physics experiment, Ming drops a baseball from the top of a 315-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t^2, which gives the distance h, in feet, that a free-falling object travels in t seconds.)
Answer: 4.4 seconds
Step-by-step explanation:
h(t) = -16t² + 315
Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0
0 = -16t² + 315
-315 = -16t²
[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]
Answer:
≈ 4.44 sec
Step-by-step explanation:
h= 315 ft
h= 16t²
315 = 16t²
t²=315/16
t=√315/16 ≈ 4.44 sec
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
given a 60 month car loan at 4.71%, explain how much your monthly payments would be for a $18,400 car and what your TOTAL COST would be given that interest.
Answer:
$23161.10
Step-by-step explanation:
Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t
Step 1: Convert months to years
60 months/12 month/year = 5 years
Step 2: Plug in known variables
A = 18400(1 + 0.0471)^5
Step 3: Solve
When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.
What are the four major categories of securities? How are they evaluated?
Answer:
Cash, Bonds, Stocks and Mutual funds
Step-by-step explanation:
The four major categories of securities are:
Cash Bonds Stocks Mutual fundsThese 4 major categories are evaluated as given below:
Cash: Cash is your normal money. You can use it to buy your everyday goods and services or invest in cash in various asset classes.Bonds: Bond is debt instrument and bonds are the agreement of debt. and bonds carry coupon rate that is (interest equivalent), tenure and final capital repayment Stocks: Ownership of stock in a company. A group (or a single) share of any company is called stock. Stock means you have some stake in the company. Mutual Funds: A mutual fund is an asset basket that can hold cash, bonds, stocks, real estate, and so on. The type and structure of mutual funds will vary depending on the client's choice of the fund manager and the category of the categoryWhich will provide the largest yield on an annuity after 30 years with 6% annual interest, compounded monthly? Annuity A: Deposit $2400 per year. Annuity B: Deposit $600 per quarter. Annuity C: Deposit $72,000 one lump sum.
Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
The cost (in dollars) of producing x units of a certain commodity is C(x) = 7000 + 6x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 103 $ per unit (ii) x = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
Answer:
The instantaneous rate is 36.
Step-by-step explanation:
Given the cost of producing a commodity,
[tex]C(x) = 7000 + 6x + 0.15x^{2}[/tex]
Now calculate the average rate of change in cost of producing commodity.
Use below formula to calculate average rate of change when (i) x = 103 $ per unit:
[tex]\text{Average rate of change} = \frac{C(103) – C(100) }{103 - 100} \\C(x) = 7000 + 6x + 0.15x^{2} \\C(100) = 7000 + 6 \times 100 + 0.15 (100)^{2} = 9100 \\C(103) = 7000 + 6 \times 103 + 0.15 (103)^{2} = 9209.35 \\\text{Average rate of change} = \frac{9209.35 - 9100}{103 - 100} = 36.45[/tex]
Now calculate average rate of change when (ii) x = 101 $ per unit:
[tex]\text{Average rate of change} = \frac{C(101) – C(100) }{101 - 100} \\C(x) = 7000 + 6x + 0.15x^{2} \\C(100) = 7000 + 6 \times 100 + 0.15 (100)^{2} = 9100 \\C(101) = 7000 + 6 \times 101 + 0.15 (101)^{2} = 9136.15 \\\text{Average rate of change} = \frac{9136.15 - 9100}{101 - 100} = 36.15[/tex]
Now to find the Instantaneous Rate of Change we just need to find the differentiation of given function.
[tex]C(x) = 7000 + 6x + 0.15x^{2} \\C’(x) = 6 + 0.3x \\[/tex]
Instantaneous Rate of Change when x = 100
[tex]= 6 + 0.3 \times (100) \\= 36[/tex]