Answers
Answer
a)
[tex]B=B_{0}(1+\frac{a}{12})^{t}[/tex]b)
[tex]B=B_{0}(1+\frac{25}{3}a)^{t}[/tex]c)
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]Explanation
We're given the function:
[tex]B=B_0(1+r)^t[/tex]To represent the equation with the data given in the problem, we need to solve the three parts of this problem.
The part a ask us to write the expression in terms of annual percentage rate (APR) in decimal. If we call "a" the APR in decimal, then the monthly rate is the APR divided in 12:
[tex]r=\frac{a}{12}[/tex]Now we can rewrite the balance equation in terms of the initial investment, the number of months and the APR:
[tex]B=B_0(1+\frac{a}{12})^t[/tex]In part b, we need to write the balance equation using the APR as percentage. The APR as decimal is equal to the APR in percentage divided by 100. If we call A the APR in percentage:
[tex]a=\frac{A}{100}[/tex]Now we replace this value in the balance equation we got in part a:
[tex]B=B_0(1+\frac{100a}{12})^t[/tex]Then simplify:
[tex]B=B_0(1+\frac{25}{3}a)^t[/tex]That's the answer to b.
In part c, we need to write the balance equation with the time in years. Since 1 year has 12 months, if we call the number of months t, and the number of years y:
[tex]t=12y[/tex]Then:
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]And this is the answer to c.
Related Questions
NEED ANSWER ASAP Solve this system of equations:3x - 2y = - 8y= 3/2x - 2I NEED ALL THE STEPS
Answers
Let's solve it by replacing in the first equation.
3x-2y=-8
y=3/2x-2
So,
3x-2(3/2x -2)=-8
3x-3x+4=-8
How to find the value of X in problem 15
Answers
We are asked to determine the value of "x" and "y".
To determine the value of "y" we will use the facto that since WP is a median this means that:
[tex]AP=PH[/tex]Substituting the values in terms of "y" we get:
[tex]3y+11=7y-5[/tex]Now, we solve for "y". To do that we will first subtract "7y" from both sides:
[tex]\begin{gathered} 3y-7y+11=7y-7y-5 \\ -4y+11=-5 \end{gathered}[/tex]Now, we subtract 11 from both sides:
[tex]\begin{gathered} -4y+11-11=-5-11 \\ -4y=-16 \end{gathered}[/tex]Now, we divide both sides by -4:
[tex]\begin{gathered} y=-\frac{16}{-4} \\ \\ y=4 \end{gathered}[/tex]therefore, the value of "y" is 4.
Now, to determine the value of "x" we will use the fact that since WP is an angle bisector we have that:
[tex]m\angle HWP+m\angle PWA=m\angle HWA[/tex]We also have the:
[tex]m\angle PWA=m\angle HWP[/tex]Therefore, we have:
[tex]\begin{gathered} m\operatorname{\angle}HWP+m\operatorname{\angle}HWP=m\operatorname{\angle}HWA \\ 2m\operatorname{\angle}HWP=m\operatorname{\angle}HWA \end{gathered}[/tex]Now, we substitute the values:
[tex]2(x+12)=4x-16[/tex]Now, we divide both sides by 2:
[tex]x+12=2x-8[/tex]Now, we subtract 2x from both sides:
[tex]\begin{gathered} x-2x+12=2x-2x-8 \\ -x+12=-8 \end{gathered}[/tex]Now, we subtract 12 from both sides:
[tex]\begin{gathered} -x+12-12=-8-12 \\ -x=-20 \\ x=20 \end{gathered}[/tex]This means that the value of "x" is 20.
To determine if WP is an altitude we need to determine if the angle APW is 90 degrees. To do that we use the fact that the sum of the interior angles of a triangle always adds up to 180, therefore:
[tex]m\angle WPA+m\angle PWA+m\angle PAW=180[/tex]We substitute the values in terms of "x":
[tex]m\angle WPA+(x+12)+(3x-2)=180[/tex]Now, we substitute the value of "x":
[tex]m\angle WPA+(20+12)+(3(20)-2)=180[/tex]Solving the operations:
[tex]m\angle WPA+90=180[/tex]now, we subtract 90 from both sides:
[tex]\begin{gathered} m\angle WPA=180-90 \\ m\angle WPA=90 \end{gathered}[/tex]Since WPA is 90 degrees and WP is a median and bisector this means that WP is an altitude.
Two weather stations are aware of a thunderstorm located at point C. The weather stations A and B are 24 miles apart.
Answers
Assuming the dashed lines are parallel and perpendicular to the base, we can start by draw a third parallel line that passes through C and naming some distances:
Now, we can see that the given angles are alternate interior angles with respect to the angles formed by the new perpendicular line and the lines AC and BC:
Now, we can see that b and the base a + 24 are related with the tangent of 48°:
[tex]\tan 48\degree=\frac{a+24}{b}[/tex]Also, b and a are related with the tangent of 17°:
[tex]\tan 17\degree=\frac{a}{b}[/tex]We can solve both for b and equalize them:
[tex]\begin{gathered} b=\frac{a+24}{\tan48\degree} \\ b=\frac{a}{\tan17\degree} \\ \frac{a+24}{\tan48°}=\frac{a}{\tan17\degree} \\ a\tan 17\degree+24\tan 17\degree=a\tan 48\degree \\ a\tan 48\degree-a\tan 17\degree=24\tan 17\degree \\ a(\tan 48\degree-\tan 17\degree)=24\tan 17\degree \\ a=\frac{24\tan17\degree}{\tan48\degree-\tan17\degree}=\frac{24\cdot0.3057\ldots}{1.1106\ldots-0.3057\ldots}=\frac{7.3375\ldots}{0.8048\ldots}=9.1162\ldots \end{gathered}[/tex]Now, we can relate a and x with the sine of 17°:
[tex]\begin{gathered} \sin 17\degree=\frac{a}{x} \\ x=\frac{a}{\sin17\degree}=\frac{9.1162\ldots}{0.2923\ldots}=31.18\ldots\approx31.2 \end{gathered}[/tex]And x is the distance between A and C, the storm. Thus the answer is approximately 31.2 miles, fourth alternative.
F (x)=x^2+4 what is f(-4)
Answers
ANSWER
f(-4) = 20
EXPLANATION
To find f(-4) we just have to replace x by -4 in function f(x):
[tex]f(-4)=(-4)^2+4[/tex]First solve the exponents. Remember that if the exponent is even and the result is always positive, either the base is positive or negative:
[tex]f(-4)=16+4=20[/tex]Convert the radical to exponential form. Assume variables represent positive real numbers.
Answers
Exponential Form of Radicals
A radical can be expressed in exponential form by using the equivalence:
[tex]\sqrt[m]{x^n}=x^{\frac{n}{m}}[/tex]We are given the expression:
[tex]\sqrt[4]{16a^4b^3}[/tex]It can be separated into several radicals:
[tex]\sqrt[4]{16a^4b^3}=\sqrt[4]{16}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3}[/tex]Now we apply the equivalence on each individual radical:
[tex]\begin{gathered} \sqrt[4]{16a^4b^3}=\sqrt[4]{2^4}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3} \\ \sqrt[4]{16a^4b^3}=2^{\frac{4}{4}}\cdot a^{\frac{4}{4}}\cdot b^{\frac{3}{4}} \end{gathered}[/tex]Simplifying:
[tex]\sqrt[4]{16a^4b^3}=2ab^{\frac{3}{4}}[/tex]Which of the following rational expressions has the domain restrictions X = -6 and x = 1?
Answers
The domain of the function is possible values of independant varaible such that function is defined or have real values.
So the expression
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]is not defined for x = -6 and for x = 1, as expression becomes undefined for this values of x (Denominator becomes 0).
So answer is,
[tex]\frac{(x+2)(x-3)}{(x-1)(x+6)}[/tex]Option B is correct.
(06.04)The line of best fit for a scatter plot is shown:A scatter plot and line of best fit are shown. Data points are located at 1 and 4, 2 and 6, 2 and 3, 4 and 3, 6 and 1, 4 and 5, 7 and 2, 0 and 6. A line of best fit passes through the y-axis at 6 and through the point 4 and 3.What is the equation of this line of best fit in slope-intercept form? (4 points)y = −6x + three fourthsy = 6x + three fourthsy = negative three fourthsx + 6y = three fourthsx + 6
Answers
Answer:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex]Explanation:
Given the y-intercept and a point, we want to get the equation of the line of best fit
We have the slope-intercept form as:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept:
[tex]y\text{ = mx + 6}[/tex]Now, to get m, we substitute the point (4,3)
We substitute 3 for y and 4 for x
We have that as:
[tex]\begin{gathered} 3\text{ = 4m + 6} \\ 3-6\text{ = 4m} \\ 4m\text{ = -3} \\ m\text{ = -}\frac{3}{4} \end{gathered}[/tex]Thus, the equation of the line of best fit is:
[tex]y\text{ = -}\frac{3}{4}x\text{ + 6}[/tex]What is the solution of the inequality shown below? 1 + a 4 enter the correct answer
Answers
We are given the following inequality:
[tex]1+a\le4[/tex]To solve this inequality we will subtract 1 to both sides:
[tex]\begin{gathered} 1-1+a\le4-1 \\ a\le3 \end{gathered}[/tex]And thus we get the solution.
Erica is given the diagram below and asked to prove that AB DF. What would be the missing step of the proof? Given: Point B is the midpoint of EF, and point A is the midpoint of ED. Prove: AB DF
Answers
Given
To find the missi
Mr. Fowler's science class grew two different varieties of plants as part of anexperiment. When the plant samples were fully grown, the studentscompared their heights.PlantvarietyHeight of plant(inches)20, 17, 19, 18, 21Mean Mean absolute deviation(Inches)Variety A191.2Variety B13, 18, 11,9,14132.4Based on these data, which statement is true?O A. The maximum height for plants from variety B is greater than forvariety A.B. Plants from variety A always grow taller than plants from variety B.C. The height of a plant from variety B is likely to be closer to themean.D. The height of a plant from variety A is likely to be closer to themean.
Answers
Let's analyze all the statements and see why they are false or true.
A. FALSE
The tallest plant in variety B is just 18 tall, while the variety A we have 21.
B. FALSE
We do have plants in A that have the same height as B.
C. FALSE
The standard deviation measure how far it's from the mean, the variety B has a 2.4 standard deviation, which means that the height can be more distant from the mean than in variety A.
D. True
Justified by C. Variety A has a 1.2 standard deviation, which means it's more likely to be closer to the mean
There are 8 triangles and 20 circles. What is the simplest ratio of triangles to circles?
Answers
Answer:
2:5
Step-by-step explanation:
8:20
= 4:10 (simplifying)
= 2:5
Answer:
2:5
Step-by-step explanation:
8=2*2*2, 20=2*2*5
cancel out the numbers they have in common
8=2*2*2, 20=2*2*5
=2,5
as a ratio
2:5
what is the GCF of 20 and 32
Answers
Given the following numbers
[tex]20,32[/tex]To find the greatest common factor, G.C.F.
The factor that can divide through two or more numbers evenly is the G.C.F
The factors of 20 and 32 are as follows
[tex]\begin{gathered} 20\Rightarrow1\times2\times2\times5 \\ 32\Rightarrow1\times2\times2\times2\times2\times2 \end{gathered}[/tex]The common factors between 20 and 32 is
[tex]\begin{gathered} \text{Common factors }=2,2 \\ G\mathrm{}C\mathrm{}F=2\times2=4 \\ G\mathrm{}C\mathrm{}F=4 \end{gathered}[/tex]Hence, the GCF of 20 and 32 is 4
Alternatively
Finding the G.C.F using table to find the G.C.F of 20 and 32
Therefore, the G.C.F is
[tex]G.C.F\Rightarrow2\times2=4[/tex]Hence, the G.C.F of 20 and 32 is 4
The number of visits to public libraries increased from 1.2 billion in 1990 to 1.6 billion in 1994. Find the average rate of change in the number of public library visits from 1990 to 1994.
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested rate of change, so we obtain the following:
We will replace in the rate of change formula with the following points: (1990, 1.2) and (1994, 1.6), then we have:
Rate of change=(f(b)-f(a))/(b-a)
Rate of change=(1.6-1.2)/(1994-1990)
Rate of change=0.4/4
Rate of change=0.1 Billion
Finally we obtain that the average rate of change in the number of public library visits from 1990 to 1994 is 0.1 billion.
a bag contains 30 marbles. 8 are pink, 11 are blue, 4 are yellow and 7 are purple. Calculate the probability of randomly selecting a marble that is not blue .
Answers
In order to find the probability of a marble not being blue, we need to find how many marbles are not blue.
To do so, we just need to sum the number of pink, yellow and purple marbles:
[tex]8+4+7=19[/tex]Now, to find the probability, we just need to divide the number of non-blue marbles by the total number of marbles.
[tex]\frac{19}{30}=0.6333=63.33\text{\%}[/tex](a) Find an angle between 0 and 2pi that is coterminal with 10pi/3.(b) Find an angle between 0° and 360° that is coterminal with -300°.Give exact values for your answers.(a) __ radians(b) __ °
Answers
To find a coterminal angle between 0 and 2pi, you can subtract 2pi from the given angle, like this
[tex]\frac{10\pi}{3}-2\pi\text{ }[/tex]To do the subtraction, you can convert 2pi into a fraction, like this
[tex]\frac{2\pi\cdot3}{3}=\frac{6\pi}{3}[/tex]So, you have
[tex]\frac{10\pi}{3}-2\pi=\frac{10\pi}{3}-\frac{6\pi}{3}=\frac{4\pi}{3}[/tex]Therefore, 4pi/3 is the angle between 0 and 2pi that y is coterminal with 10pi/3.
For point (b), you can add 360° at the angle given, like this
[tex]360+(-300)=360-300=60[/tex]Therefore, an angle between 0° and 360° that is coterminal with -300° is 60°.
Graph AABC with A(4, 7), B(0,0), and C(8, 1).a. Which sides of AABC are congruent? How do you know?b. Construct the bisector of ZB. Mark the intersection of the ray and AC as D.c. What do you notice about AD and CD?
Answers
a) Two sides of a triangle are concruent when they are the same length. First calculate the lenght of each side
[tex]\begin{gathered} AC^2=\text{ (X\_c-X\_a)}^2+(Y_a-Y_c)^2=(8-4)^2+(7-1)^2=\text{ 52} \\ AC=\sqrt{52}=7.2 \end{gathered}[/tex][tex]\begin{gathered} AB^2=(X_a-X_b)^2+(Y_a-Y_b)^2=(4-0)^2+(7-0)^2=\text{ 65} \\ AB=\sqrt{65}=8.06\approx8 \end{gathered}[/tex][tex]\begin{gathered} BC^2=(X_c-X_b)^2+(Y_c-Y_b)^2=(8-0)^2+(1-0)^2=\text{ 65 } \\ BC=\sqrt{65}=8.06\approx8 \end{gathered}[/tex]Sides AB and BC aren congruent.
b)
The bisector divides the triangle in exact halves.
The bisector is the blue line, in green you'll se the length of each side.
c)
Which is the greatest number?A. 50 – 16piB. 16 - sqrt(410)C. -sqrt(20) + 1/2D. 7/3 - (7pi/3)فر
Answers
First, we need to develop each case or take care of the following:
One number is greater than another if it is more at the right of the Real Line.
A negative number is lower than a positive number.
Between two negative numbers, the greater is the one near to zero.
Let develop the numbers:
A. 50 - 16pi is approximately -0.265472
B. 16 - sqrt(410) approximately equals to -4.24845
C. -sqrt(20) + 1/2 is approximately equals to -3.97213
D. 7/3 - (7*pi)/3 is approximately equaled to -4.99705
So taking into account the previous reasons at the beginning, we have that the number near to zero is -0.265472, which is the first option. Option A.
Given the following data, find the diameter that represents the 69th percentile.AnswerHow to enter your answer (opens in new window)Diameters of Golf Balls1.531.36 1.69 1.68 1.701.601.601.361.34 1.531.32 1.401.39 1.391.44
Answers
Given that there is a Table given of diameters
How does g(t) = 1/2t change over the interval t = 0 to t = 1?
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we have the equation
[tex]g(t)=\frac{1}{3^t}[/tex]Find out the rate of change over the interval [0,1]
Remember that
the formula to calculate the rate of change is equal to
[tex]\frac{g(b)-g(a)}{b-a}[/tex]In this problem
a=0
b=1
g(a)=g(0)=1
g(b)=g(1)=1/3
therefore
the function decreases by a factor of 32-18 72 20=34-To=315)-10=35 5)EXTENSION: a) In right A DEF, m D = 90 and mZF is 12 degrees less than twice mze. Find mZE. b) in AABC, the measure of ZB is 21 less than four times the measure of LA, and the measure of ZC is 1 more than five times the measure of ZA. Find the measure, in degrees, of each angle of ABC.
Answers
As given by the question
There are given that in the right triangle DEF, angle D is 90 degrees and angle f is 12 degrees less than angle E.
Now,
The sum of the three measures of a triangle is always 180 degree
So,
[tex]m\angle D+m\angle E+m\angle F=180[/tex]Where angle D is 90 degree
Then,
[tex]\begin{gathered} m\angle D+m\angle E+m\angle F=180 \\ 90+m\angle E+m\angle F=180 \\ m\angle E+m\angle F=90 \end{gathered}[/tex]Also we are given that
[tex]\begin{gathered} F+12=2E \\ F=2E-12 \end{gathered}[/tex]Therefore, substituting for F back into E+F=90
Then,
[tex]\begin{gathered} E+(2E-12)=90 \\ 3E-12=90 \\ 3E=102 \\ E=34 \end{gathered}[/tex]So, angle E is 34 degrees, which is the answer.
Complete the coordinate proof. Answer choices are on the bottom.
Answers
Given:
There are given that the triangle, ABC.
Where:
[tex]\begin{gathered} A=(3,6) \\ B=(5,0) \\ C=(1,0) \end{gathered}[/tex]Explanation:
According to the question, we need to prove that the isosceles triangle:
So,
From the concept of the isosceles triangle:
The isosceles triangle is defined when two sides of the length of any triangle are equal.
Then,
First, we need to find the length of the sides by using the distance formula:
So,
[tex]\begin{gathered} AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AB=\sqrt{(5-3)^2+(0-6)^2} \\ AB=\sqrt{(2)^2+(-6)^2} \\ AB=\sqrt{4+36} \\ AB=\sqrt{40} \end{gathered}[/tex]Then,
[tex]\begin{gathered} AC=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AC=\sqrt{(1-3)^2+(0-6)^2} \\ AC=\sqrt{(-2)^2+(-6)^2} \\ AC=\sqrt{4+36} \\ AC=\sqrt{40} \end{gathered}[/tex]And,
[tex]\begin{gathered} CB=\sqrt{(5-1)^2+(0-0)^2} \\ CB=\sqrt{(4)^2+0} \\ CB=4 \end{gathered}[/tex]Final answer:
Hence, the step and values of the sides are shown below;
[tex]\begin{gathered} CA=d \\ AB=d \end{gathered}[/tex]And,
The side CA and AB is congruence by the definition of h
And,
Triangle ABC is an isosceles triangle by the the defination of b.
If cos(0) = 24/25, and 0 is in Quadrant I, then what is cos(0/2)? Simplify your answer completely, rationalize the denominator, and enter it in fractional form.
Answers
The given information is:
[tex]\begin{gathered} \cos (\theta)=\frac{24}{25} \\ \theta\text{ is in quadrant I} \end{gathered}[/tex]cos (theta/2) is given by:
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]In Quadrant I, cos (theta) is positive, then the answer is positive. By replacing the known values:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{25+24}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{49}{25}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{25\times2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{49}{50}} \\ \cos (\frac{\theta}{2})=\frac{\sqrt[]{49}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7}{\sqrt[]{50}}\cdot\frac{\sqrt[]{50}}{\sqrt[]{50}} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{50}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{25\times2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot\sqrt[]{25}\cdot\sqrt[]{2}}{50} \\ \cos (\frac{\theta}{2})=\frac{7\cdot5\cdot\sqrt[]{2}}{50} \\ \text{Simplify 5/50} \\ \cos (\frac{\theta}{2})=\frac{7\sqrt[]{2}}{10} \end{gathered}[/tex]Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your reasoning.
Answers
The given angle and angle 3 are corresponding angles, that is, angles that are on the same corner at each intersection. Graphically,
Corresponding angles are congruent, so
[tex]\angle3=95\text{\degree}[/tex]On the other hand, angle 3 and angle 4 are supplementary angles, that is, add up to 180°. Graphically,
[tex]A+B=180\text{\degree}[/tex]So, you have
[tex]\begin{gathered} \angle3+\angle4=180\text{\degree} \\ 95\text{\degree}+\angle4=180\text{\degree} \\ \text{ Subtract 95\degree from both sides of the equation} \\ 95\text{\degree}+\angle4-95\text{\degree}=180\text{\degree}-95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}[/tex]Therefore, the measures of the numbered angles are
[tex]\begin{gathered} \angle3=95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}[/tex]Last weekend, 5% of the tickets sold at Seaworldwere discount tickets. If Seaworld sold 60 tickets inall, howmany discount tickets did it sell? Use thepercent proportion.
Answers
Let:
N = Total tickets
d = discount tickets
r = percent of discount tickets sold
so:
[tex]\begin{gathered} d=N\cdot r \\ where\colon \\ N=60 \\ r=0.05 \\ so\colon \\ d=60\cdot0.05 \\ d=3 \end{gathered}[/tex]3 discount tickets were sold
Ingrid deposits $10,000 in an IRA. What will be the value of her investment in 6 years if the investment is earning 3.2% per year and is compounded continuously? Round to the nearest cent.
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We have a initial deposit of $10,000 (PV=10,000).
The investment last 6 years (t=6).
The annual interest rate is 3.2% (r=0.032) and is compounded continously.
The equation to calculate the future value FV of the inverstment for this conditions is:
[tex]\begin{gathered} FV=PV\cdot e^{rt} \\ FV=10,000\cdot e^{0.032\cdot6} \\ FV=10,000\cdot e^{0.192}. \\ FV\approx10,000\cdot1.2116705 \\ FV\approx12,116.71 \end{gathered}[/tex]The value of her investment will be $12,116.71.
1 8. Dee Saint earns a monthly salary of $750 plus a 6% commission on all sales over $1,000 each month. Last month, her sales were $5,726. What was her income for the month?
Answers
Her monthly income for last month was $1,093.56
Here, we want to calculate the monthly income for Dee Saint
Mathematically, from the information given in the question, we can have this as;
[tex]\begin{gathered} 750\text{ + 6\% of \$5726} \\ \\ =\text{ 750 + 0.06(5726)} \\ \\ =\text{ 750 + 343.56} \\ \\ =\text{ \$1,093.56} \end{gathered}[/tex]9. Find the volume of the triangular pyramid. (2pts)-10 mI9 m16 m
Answers
Answer:
240 m³
Explanation:
The volume of a pyramid is equal to:
[tex]V=\frac{1}{3}\times B\times H[/tex]Where B is the area of the base and H is the height of the pyramid.
Then, the base of the pyramid is a triangle, so the area of a triangle is equal to:
[tex]B=\frac{b\times h}{2}[/tex]Where b is the base of the triangle and h is the height of the triangle. So, replacing b by 16 m and h by 9 m, we get:
[tex]B=\frac{16\times9}{2}=\frac{144}{2}=72m^2[/tex]Finally, replacing B by 72 m² and H by 10 m, we get that the volume of the pyramid is equal to:
[tex]V=\frac{1}{3}\times72\times10=\frac{1}{3}\times720=240m^3[/tex]Therefore, the volume is 240 m³
For each ordered pair, determine whether it is a solution to the sytem of equations.
Answers
Given
We have the system of equations:
[tex]\begin{gathered} 3x\text{ - 2y = -4} \\ 2x\text{ + 5y = -9} \end{gathered}[/tex]The ordered pair that would be a solution to the given system of equations must satisfy both equations. There can only be one ordered pair and this can be obtained by solving the system of equations simultaneously
Using a graphing tool, the plot of the lines is shown below:
The point where the lines intercept is the solution to the system of equations.
Hence the ordered pair that is a solution is (-2, -1)
Answer:
(4,8) - No
(8, -5) - No
(0, 3) - No
(-2, -1) - Yes
8Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.p=(-c ≤ Z ≤ c ) =0.9127Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answers
The value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
It is given to us that -
[tex]P(-c\leq Z\leq c)=0.9127[/tex] is true
It is also given that Z follows the standard normal distribution.
We have to find out the value of c.
Since Z follows the standard normal distribution, so we can say that
Z ∼ N(0,1)
To find out c,
[tex]P(-c\leq Z\leq c)=0.9127\\= > P(Z\leq c)-P(Z\leq -c)=0.9127\\[/tex]
Since there is a symmetric z-distribution, the above equation can be represented as -
[tex][1-P(Z\leq -c)]-P(Z\leq -c) = 0.9127\\= > 1-P(Z\leq -c) - P(Z\leq -c) = 0.9127\\= > 1-2P(Z\leq -c)=0.9127\\= > 2P(Z\leq -c)=0.0873\\= > P(Z\leq -c)=0.04365[/tex]
=> -c ≈ 0.0873 (Using online calculator)
Therefore, the value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
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Answer:
The value of c such that is true is 0.0873 where Z follows the standard normal distribution.
Step-by-step explanation:
Simplify. Final answer should be in standard form NUMBER 18
Answers
4(2 - 3w)(w^2 - 2w + 10) =
(8 - 12w)(w^2 - 2w + 10) =
8w^2 - 16w + 80 - 12w^3 + 24w^2 - 120w =
- 12w^3 + 32w^2 - 123w + 80