The question ask to evaluate the expression:
[tex]9^{-\frac{5}{2}}[/tex]Step 1: Factor the number
[tex]9=3^2[/tex]Therefore, the expression becomes:
[tex]\Rightarrow(3^2)^{-\frac{5}{2}}[/tex]Step 2: Apply the exponent rule given to be
[tex](x^a)^b=x^{a\times b}[/tex]Therefore, we have:
[tex]\Rightarrow(3^2)^{-\frac{5}{2}}=3^{2\times-\frac{5}{2}}=3^{-5}[/tex]Step 3: Apply the exponent rule given to be
[tex]x^{-a}=\frac{1}{x^a}[/tex]Therefore, the expression becomes:
[tex]3^{-5}=\frac{1}{3^5}[/tex]Step 4: Calculate
[tex]3^5=243[/tex]Therefore, we have
[tex]\frac{1}{3^5}=\frac{1}{243}[/tex]ANSWER
[tex]9^{-\frac{5}{2}}=\frac{1}{243}[/tex]Find the intercepts of the function.g(n) = −3(3n − 1)(4n + 1)n-intercept (n, g(n)) = (smaller n-value)n-intercept (n, g(n)) = (larger n-value)y-intercept (n, g(n)) =
In order to find the n-intercepts of the function, let's equate each factor to zero:
[tex]\begin{gathered} -3(3n-1)(4n+1)=0\\ \\ \begin{cases}3n-1=0\rightarrow n=\frac{1}{3}{} \\ 4n+1=0\rightarrow n=-\frac{1}{4}{}\end{cases} \end{gathered}[/tex]So the n-intercept with the smaller n-value is (-1/4, 0) and the n-intercept with the larger n-value is (1/3, 0).
Now, to find the y-intercept, let's use n = 0 and calculate the value of g(n):
[tex]\begin{gathered} g(n)=-3(3n-1)(4n+1)\\ \\ g(0)=-3(3\cdot0-1)(4\cdot0+1)\\ \\ g(0)=-3(-1)(1)\\ \\ g(0)=3 \end{gathered}[/tex]Therefore the y-intercept is (0, 3).
Yasin performs the elementary row operation represented by R2 - ½ R1 on matrix A.
We are given a matrix of
[tex]\begin{bmatrix}{4} & {3} & {0} \\ {-6} & {-3} & {12} \\ {} & {} & \end{bmatrix}[/tex]Yasin performs R2 - 1/2R1
The second row and column will be
For the first row
-6 - 1/2(4)
-6 - 2
= -8
For the second row
-3 - 1/2(3)
= -3 -3/2
= -2 * 3 / 1 - 3 x 2 / 2 / 2
= -6 - 3 / 2
= -9/2
Third row
12 - 1/2(0)
= 12 - 0
12
The new matrix is
[tex]\begin{bmatrix}{4} & {3} & {0} \\ {-8} & {-\frac{9}{2}} & {12} \\ {} & {} & {}\end{bmatrix}[/tex]Inverse of an exponential function fill in the chart. If needed, use a calculator and round to one decimal place.
ANSWER :
The answers from column to column are :
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=e^x[/tex]The first column is the value of f(x) at given x values.
The second column is also the value of f(x) but written as a point (x, f(x))
The third column is the inverse of the function written as a point (f(x), x)
We will solve this from one column to another column.
That will be :
[tex]\begin{gathered} \text{ when x = 0} \\ f(0)=e^0=1 \\ (x,f(x))=(0,1) \\ (f(x),x)=(1,0) \\ \text{ The answers are g, h and s} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = 1} \\ f(1)=e^1\approx2.7 \\ (x,f(x))=(1,2.7) \\ (f(x),x)=(2.7,1) \\ \text{ The answers are e, a and b} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = -1} \\ f(-1)=e^{-1}\approx0.4 \\ (x,f(x))=(-1,0.4) \\ (f(x),x)=(0.4,-1) \\ \text{ The answers are d, q and r} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = 2} \\ f(2)=e^2\approx7.4 \\ (x,f(x))=(2,7.4) \\ (f(x),x)=(7.4,2) \\ \text{ The answers are k, f and c} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = -2} \\ f(-2)=e^{-2}\approx0.1 \\ (x,f(x))=(-2,0.1) \\ (f(x),x)=(0.1,-2) \\ \text{ The answers are m, l and n} \end{gathered}[/tex]g, h and s
Michael wanted to make chocolate milk. He used proportional reasoning based on the table. If his glassonly holds 2.5 cups, how many tablespoons of chocolate syrup does he need?
First, we find the ratio between the cups of mils and the tablespoons of chocolate syrup
[tex]\frac{6}{4}=1.5[/tex]The ratio is 1.5, which means we have to multiply this ratio by 2.5 cups.
[tex]2.5\times1.5=3.75[/tex]So, Michael needs 3.75 tablespoons of chocolate syrup to its 2.5 cups glass.
Is there a proportional relationship between x and y? Explain. if you would like the options let me know!!
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y=kx
for some constant k , called the constant of proportionality .This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
Here, as the ratios x/y and y/x are not folowed, through all the sets of x and y, it is not a proportional relationship.
Thus, first option is correct
3/5 greater or least 7/10. I need to use compare fractions common numerator
We have the following fractions
[tex]\frac{3}{5}\text{ and }\frac{7}{10}[/tex]We know that if the denominators of two fractions are the same then the fraction with the largest numerator is the larger fraction.
Then, we need to convert the denominator of one fraction so they both have the same denominator. For instance, if we multiply and divide by 2 the first fraction, we have an equivalent fraction, that is,
[tex]\frac{3}{5}=\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}[/tex]This means that 3/5 is equivalent to 6/10 but in the last form 6/10 and 7/10 have the same denominator, so we can compare their numerators. In other words, we need to compare
[tex]\frac{6}{10}\text{ and }\frac{7}{10}[/tex]Since 7 is greater than 6 then:
[tex]\frac{3}{5}<\frac{7}{10}[/tex]Instead of converting 3/5, we can convert the fraction 7/10. If we multiply and divide 7/10 by 1/2, we have
[tex]\frac{7}{10}=\frac{\frac{7}{2}}{\frac{10}{2}}=\frac{3.5}{5}[/tex]Now, we can compare these fractions:
[tex]\begin{gathered} \frac{3}{5}\text{ and }\frac{3.5}{5} \\ \sin ce\text{ 3.5 is greater that 3, then} \\ \frac{3}{5}<\frac{7}{10} \end{gathered}[/tex]A box of light bulbs is shipped to a hardware store. When it arrives, 4 of the bulbs are broken. Predict the number of broken light bulbs in an order of 125 bulbs.
As 4 of 25 light bulbs are broken you use a rule of three to find the number of broken bulbs in a order of 125:
[tex]x=\frac{125\cdot4}{25}=\frac{500}{25}=20[/tex]Then, in a order of 125 bulbs the prediction is 20 broken bulbsWhen Paisley moved into a new house, she planted two trees in her backyard. At thetime of planting, Thee A was 21 inches tall and Tree B was 33 inches tall. Each yearthereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. LetA represent the height of Tree At years after being planted and let B represent theheight of Tree Bt years after being planted. Write an equation for each situation, interms oft, and determine the interval of time, t, when Tree A is taller than Tree B.A= 21 + 6t – 6B = 33 + 3t-3Tree A is taller than Tree B whentNote: The interval will only apply for valid values oft in the domainSubmit Answer
Tree A
[tex]A=21+6t[/tex]Tree B
[tex]B=33+3t[/tex]To determine the interval, we must write that A is greater than B with an inequality
[tex]A>B[/tex]OR
[tex]21+6t>33+3t[/tex]and solve t
[tex]\begin{gathered} 6t-3t>33-21 \\ 3t>12 \\ t>\frac{12}{3} \\ t>4 \end{gathered}[/tex]so, the interval is
[tex](4,\infty)[/tex]Y=x^2-6x+2 in vertex form and show work
The vertex form is
[tex]Y=\mleft(x-3\mright)^2-7[/tex]The form of the equation given is: Y=ax^2+bx+c
So, a=1, b=-6 and c=2
The vertex form is
[tex]Y=a\mleft(x-h\mright)^2+k[/tex]Where
[tex]h=\frac{-b}{2a}\text{ , and k=f(h)}[/tex]Then
[tex]h=\frac{-b}{2a}=\frac{-(-6)}{2\cdot1}=3[/tex][tex]k=f(h)=f(3)=(3)^2-6\cdot3+2[/tex]Then, using a,h and k:
[tex]Y=(x-3)^3-7[/tex]help the answers are CPCTC Definition of congruence SAS and SSS
SOLUTION
From the question given the following statements to prove are correct, then the last part
[tex]\Delta RSU\cong\Delta TSV[/tex]The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem
Question 4The members of the high school swim team are in ratio of 4 boys to every 3 girls. Howmany boys are there if there are 15 girls on the team?on't knowOne attempt157wered 3 out of 3 correctly. Asking up to 9.204
hello
from the question given, we know the ratio between the boys to the girls are 4:3 and the number of girls are 15 on the team
[tex]b=\frac{15}{3}\times4=5\times4=20[/tex]the numbers of boys on the team are 20
Calculate an estimate for the maximum number of drinks a 110lb female can consume without going over 0.08 BAC if she plans on leaving the party in 2 hours.
we have the following:
The formula is:
[tex]B=-0.015\cdot t+\frac{2.84\cdot N}{W\cdot g}[/tex]replacing,
where
B is blood alcohol content
t is the time
N is the maximum number of drinks
W is the weight
and g a gender constant (0.55 for wormen)
[tex]\begin{gathered} 0.08=-0.015\cdot2+\frac{2.84\cdot N}{110\cdot0.55} \\ \\ 0.08=-0.03+0.0469N \\ N=\frac{0.08+0.03}{0.0469} \\ N=2.34\cong2 \end{gathered}[/tex]therefor,e th
i don’t understand what the term one to one means
From the given functions, let's select the functions that are one-to-one functions.
A function is said to be a one-to-one function when it produces different outputs for different inputs (values of x).
The easiest way to determine if a function is a one-to-one function is to graph the function and use the horizontal line test.
Now, let's check the functions to determine.
• Function 1.
f(x) = x³ - 7
Since the leading exponent is an odd number, this function can be said to be a one-to-one function.
• Function 2.
f(x) = x² - 4
The leading exponent of this function is an even number. Since it is even, it will fail the horizontal line test. Therefore, the function is NOT a one-to-one function.
• Function 3.
[tex]f(x)=\frac{1}{8x-1}[/tex]This function is a one-to-one function.
• Function 4.
[tex]f(x)=\frac{5}{x^4}[/tex]This function is a one-to-one function.
• Function 5.
f(x) = |x|
This function is NOT a one-to-one function since it will fail the horizontal line test.
Therefore, the functions that are one-to-one are:
[tex]\begin{gathered} f(x)=x^3-7 \\ \\ f(x)=\frac{1}{8x-1} \\ \\ f(x)=\frac{5}{x^4} \end{gathered}[/tex]A farmer looks over a field and sees 36 heads and 102 feet. Some are pigs, some are geese. How many of each animal are there?
There are:
36 heads and 102 feet.
The total number of animals (pigs+geese) are 36, also we know that the pigs have 4 feet and the geese 2.
Therefore, the equations to find it will be:
1. For the heads:
[tex]36=p+g\text{ \lparen1\rparen}[/tex]For the feet:
[tex]102=(4*p+2*g)\text{ \lparen2\rparen}[/tex]Where p=pigs and g= geese.
Solving the equations using substitution method:
Isolating p in (1):
[tex]36-g=p\text{ \lparen3\rparen}[/tex]Substituing (3) in (2):
[tex]\begin{gathered} 102=4p+2g \\ 102=4(36-g)+2g \end{gathered}[/tex]Solving for g:
[tex]\begin{gathered} 102=144-4g+2g \\ 102-144=-2g \\ -42=-2g \\ g=\frac{42}{2}=21 \end{gathered}[/tex]Finally, putting g=21 in (3):
[tex]\begin{gathered} p=36-g \\ p=36-21=15 \end{gathered}[/tex]Answer: There are 15 pigs and 21 geese.
Conver 9°18'42" to a decimal number of degrees.Do not round any intermediate computations.Round your answer to the nearest thousandth.
To convert from degrees to decimal, we use the formula shown below:
[tex]DD=d+\frac{\min}{60}+\frac{\sec}{3600}[/tex]Where
DD is the decimal degree
d is the degree (whole) in original degree/min/sec given
min is the minutes
sec is the number of seconds
Now,
Given,
d = 9
min = 18
seconds = 42
We substitute and find out the answer:
[tex]\begin{gathered} DD=d+\frac{\min}{60}+\frac{\sec}{3600} \\ DD=9+\frac{18}{60}+\frac{42}{3600} \\ DD=9+0.3+0.011666 \\ DD=9.311666 \end{gathered}[/tex]Rounding the answer to nearest thousandth (3 decimal places):
DD = 9.312simply the expression using rational exponents (4x^3)^1/2
The equation is given
[tex](4x^3)^{\frac{1}{2}}[/tex]Solving the expression,
[tex](2)^{\frac{1}{2}\times2}\times x^{\frac{3}{2}}=2x^{\frac{3}{2}}[/tex]The answer is
[tex]2x^{\frac{3}{2}}[/tex]express as a single power: -(8)^5 x (-8)^10
Answer:
[tex]-8^{15}[/tex]Step-by-step explanation:
Using the product of powers rules, which is represented as:
[tex]a^m*a^n=a^{m+n}[/tex]Therefore, for the given expression:
[tex]-8^5*-8^{10}=-8^{5+10}=-8^{15}[/tex]Consider 0.3 x 0.1.How many digits after the decimal point will the product have?Numbers of digits =
In this case the number of digits after the decimal pointmust be 2 because each number has one digit after the decimal point.
It takes Maggie 12 minutes to walk to school. How many hours does it take to walk to school and back? ( 5 school days per week)
Maggie spends 12 minutes per trip, in one day she makes 2 trips and we are asked to calculate how many hours she spends on these trips in 5 days
First, we will do this calculation in minutes
[tex]12\cdot2\cdot5=120[/tex]She spends 120 minutes per week, now let's do the unit conversion, converting the minutes to hours, let's remember that one hour is the same as 60 minutes.
[tex]120\min \cdot\frac{1hr}{60\min }=2hr[/tex]The answer is 2 hours
Let X be a random variable with the following distribution. If E(X) = 108, then x2=
To obtain the value of x2, the following steps are necessary:
Step 1: Recall the formula for E(X) from probability theory, as follows:
From probability theory:
[tex]E(X)=\sum ^n_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2)+\cdots+X_n\cdot P(X_n)[/tex]Step 2: Apply the formula to the problem at hand to obtain the value pf x2, as follows:
[tex]\begin{gathered} \text{Given that:} \\ E(X)=108 \\ X_1=80,P(X_1)=0.3 \\ X_2=?,P(X_2)=0.7 \end{gathered}[/tex]We now apply the formula, as below:
[tex]\begin{gathered} E(X)=\sum ^2_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \text{Thus:} \\ E(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \Rightarrow108=(80)\times(0.3)+X_2\times(0.7) \\ \Rightarrow108=24+X_2\times(0.7) \\ \Rightarrow108-24=X_2\times(0.7) \\ \Rightarrow84=X_2\times(0.7) \\ \Rightarrow X_2\times(0.7)=84 \\ \Rightarrow X_2=\frac{84}{(0.7)}=120 \\ \Rightarrow X_2=120 \end{gathered}[/tex]Therefore, the value of x2 is 120
An old dot-matrix printer took 11 minutes to print 2.5 pages. If 12 pages are going to be printed, how many minutes should this take?
We can use the following rate to solve the exercise.
[tex]\frac{11\text{ minutes}}{2.5\text{ pages}}=\frac{x}{12\text{ pages}}[/tex]Now, we solve for x:
[tex]\begin{gathered} \text{ Multiply by 12 pages from both sides} \\ \frac{11\text{ minutes}}{2.5\text{ pages}}\cdot12\text{ pages}=\frac{x}{12\text{ pages}}\cdot12\text{ pages} \\ \frac{11\text{ minutes }\cdot12\text{ pages}}{2.5\text{ pages}}=x \\ \frac{11\cdot12}{2.5}\text{ minutes}=x \\ \frac{132}{2.5}\text{ minutes}=x \\ 52.8\text{ minutes }=x \end{gathered}[/tex]AnswerThe old dot-matrix printer should take 52.8 minutes to print 12 pages.
Question 11 ptsConsider the inequality -15%A. Predict which values of x will make the inequality true and write your prediction inthe box.B. Create the table in your scratch paper to check your prediction. Were you correct?Why or why not?-4-3-2-101234
Solve the inequality for x
[tex]\text{ x }\ge\text{ -2}[/tex]Values of x that will the inequality true are -1, 0, 1 , 2, 3, 4, etc
b)
[tex]\text{ }\frac{-4}{2}\text{ = -2 }\ge\text{ -1 false}[/tex][tex]\text{ }\frac{-3}{2}\text{ }\ge\text{ -1 false }[/tex][tex]\text{ }\frac{-2}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{-1}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{0}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{1}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{2}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{3}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{4}{2}\text{ }\ge\text{ -1 true}[/tex]
A bag contains 8 red balls and 3 blue balls. Two balls are drawn at random one after the other without replacement. Find the probability that the balls drawn are red.
First, we need to calculate the probability of drawing a red ball the first time. This is given by the usual probability:
[tex]P_{\text{red}1}=\frac{\text{red }}{total}=\frac{8}{11}[/tex]Now, as for the second time we pick a ball. Notice that the number of balls in the bag has changed since there is 1 red ball less. So, the probability of extracting a red ball under these conditions is:
[tex]P_{\text{red}2}=\frac{red}{\text{total}}=\frac{7}{10}[/tex]Notice that now the total number of balls is 10 and there are 7 red ones.
Finally, the probability we are looking for is given below:
[tex]P_{\text{red}1}\cdot P_{\text{red}2}=\frac{8}{11}\cdot\frac{7}{10}=\frac{56}{110}\approx0.50909\ldots\approx0.51[/tex]The probability is the above expression, in case you need it expressed as a fraction or a decimal number.
Find f(–2), if f(x) = −3x^2 – 5x + 11
To solve the exercise, replace x = -2 in the function and operate, like this
[tex]\begin{gathered} f\mleft(x\mright)=-3x^2-5x+11 \\ f(-2)=-3(-2)^2-5(-2)+11 \\ f(-2)=-3\cdot4+10+11 \\ f(-2)=-12+10+11 \\ f(-2)=9 \end{gathered}[/tex]Therefore, the value of the function is 9 when x = -2.
Scatterplot help with problem C (8.5 million dollars,10.2million dollars,11.9million dollars,13.6million dollars, 15.3 million dollars)
ANSWER :
10.2 million dollars
EXPLANATION :
For C, we just need to locate the revenue of 50 million dollars and reflect it to the rental revenue.
It is around 10 million dollars.
From the choices, 10.2 million dollars is the closest.
What is the measure of angle x for this ramp?
1) Let's find out the angle x, using trigonometric ratios. So since we have the opposite leg to angle x and the adjacent leg to angle x we can write out that:
[tex]\sin (X)=\frac{1}{12}[/tex]2) But since we want to know the angle, so we need to calculate the arcsine of (x):
[tex]undefined[/tex]The top thing is question my answer is in the box am I correct and can you show me how to do it right if not
Formula
[tex]M=\frac{pm(1+m)^{na}}{(1+m)^{na}-1}[/tex]Given parameters
[tex]\begin{gathered} p=3,500 \\ m=\frac{8}{12\times100}=\frac{0.08}{12} \\ n=12\text{ } \\ a=2 \end{gathered}[/tex]Substitute the given parameters into the formula
[tex]M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1}[/tex][tex]\begin{gathered} M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1} \\ \\ \text{Remove the parent}heses\text{ (a)=a} \\ \frac{3500\cdot\frac{0.08}{12}\left(1+\frac{0.08}{12}\right)^{24}}{\left(1+\frac{0.08}{12}\right)^{24}-1} \\ \\ \text{Now} \\ \frac{3500\cdot\frac{0.08}{12}\mleft(\frac{0.08}{12}+1\mright)^{24}}{1.0066^{24}^{}-1} \\ \text{Multiply the numerator} \\ \frac{27.367}{1.00666^{24}-1} \\ \text{simplify} \\ =\frac{27.36738}{0.17288}=158.296 \\ \end{gathered}[/tex]The final answer
[tex]\text{ \$158.30}[/tex]Do you know what 6.756 x 108.62 is?
Evaluate the produt of decimal number 6.756 and 108.62.
[tex]\begin{gathered} 6.756\times108.62=\frac{6756}{1000}\times\frac{10862}{100} \\ =\frac{6756\cdot10862}{1000\cdot100} \\ =\frac{73383672}{100000} \\ =733.83672 \end{gathered}[/tex]So answer is 733.83672.
(A) how many cubic meters of sand can the sandbox hold? (B) the manufacture suggested the sandbox should be filled to 89% capacity. How many cubic meters of sand is this?
To solve this problem, we must find the volume of the sandbox.
[tex]V=l\cdot w\cdot d[/tex]Where:
[tex]\begin{gathered} l=30m \\ w=26m \\ d=4m \end{gathered}[/tex]Now, we replace and solve:
[tex]\begin{gathered} V=30m\cdot26m\cdot4m \\ V=3120m^3 \end{gathered}[/tex]The A answer is 3120 cubic meters
Now, for question "b" we must find how many cubic meters are 89% of its capacity, that is 89% of the capacity of the 3120 cubic meters.
For this, we multiply the total capacity of the sandbox by 0.89.
[tex]3120\cdot0.89=2776.8[/tex]The A answer is 2776.8 cubic meters
you were given a rectangle with dimension of length equals 60 inches and width equals 4J the perimeter of the rectangle is 400 in what is the value of j
Given data:
The given length of the rectangle is L=60 inches.
The given width of the rectangle is bB=4J.
The perimeter of the rectangle is P=400 inches.
The expression for the perimeter of the rectangle is,
P=2(L+B)
Substitute the given values in the above expression.
400 inches=2(60 inches+4J)
200 inches=60 inches+4J
140 inches=4J
J=35 inches
Thus, the value of J is 35 inches.