We have the following equation of the area of a square:
[tex]A=s^2[/tex]where s is the length of the side.
In this case, we have that the area is 36 square meters, then:
[tex]\begin{gathered} A=36m^2=s^2 \\ \Rightarrow s^2=36 \end{gathered}[/tex]if we apply the square root on both sides we get:
[tex]\begin{gathered} \sqrt[]{s^2}=\sqrt[]{36}=6 \\ \Rightarrow s=6 \end{gathered}[/tex]therefore, the measure of the side of the square is 6 meters
Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81
Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:
[tex]P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)[/tex]Using the values reported on tables for the standardized normal distribution, we know that:
[tex]\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}[/tex]Now, using these results:
[tex]P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507[/tex]2/5 x 2/3???????????
hello
to solve this question, we simpply need to multiply both fractions
[tex]\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]from the calculation above, the value of answer is 4/15
if 15 pizza cost $195. how much will 100 pizza cost?
15 pizza ---> $195
100 pizza --> x
[tex]\begin{gathered} 15\times x=100\times195 \\ 15x=19500 \\ \frac{15x}{15}=\frac{19500}{15} \\ x=13000 \end{gathered}[/tex]answer:
$13000
if f(x) = 3x⁴ + x² + 3 then what is the remainder when f(x) is divided by x + 1
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).
Find the value of c using the given chord and secant lengths in the diagram shown to right . c= (Round to the nearest tenth as needed .)
ANSWER
c = 6.4
EXPLANATION
The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:
[tex]9\cdot(9+19)=13\cdot(13+c)[/tex]Solving for c:
[tex]\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=\frac{83}{13} \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}[/tex](a) Approximate the population mean and standard deviation of age for males And For females.
1) Since we have a table for grouped data, we need to place into that table another column with the middle point of each interval to get the mean.
2) Setting that table with another column we've got:
Age Middlepoint Male Female Male*freq Female*fr
0-9 (0+9)/2 =4.5 10 9 10*4.5=45 9*4.5=40.5
10-19 (10+19)/2=14.5 11 5 159.5 72.5
20-29 (20+29)/2= 24.5 12 13 294 318.5
30-39 (30+39)/2= 34.5 16 19 552 655.5
40-49 (40+49)/2= 44.5 25 21 1112.5 934.5
50-59 (50+59)/2= 54.5 20 24 1090 1308
60-69 (60+69)/2=64.5 18 18 1161 1161
70-79 (70+79)/2= 74.5 15 14 117.5 1043
Now, we can pick the absolute frequency of males and females and multiply by the middle point.
Now we can add the number of males multiplied by the frequency and divide them by the sum of the frequencies, this way:
[tex]\mu=\frac{45+159.5+294+552+1112.5+1090+1161+117.5}{10+11+12+16+25+20+18+15}\approx38.68[/tex]3) Now to find the standard deviation of this population, we can write out the following:
[tex]\begin{gathered} \sigma=\frac{\sqrt[]{(45-38.68)^2+(159.5-38.68)^2+(294-38.68)^2+(552-38.68)^2+(1112.5-38.68)^2+(1090-38.68)^2+(1161-38.68)^2+(117.5-38.68)^2}}{8} \\ \\ \sigma=452.6694 \end{gathered}[/tex]Marcus hikes at a rate of 2 1/9 miles per hour. If he hikes for 6 hours, how many miles will he hike?
We have the following:
let s is speed, d is distance and t is time, therefore:
[tex]\begin{gathered} s=\frac{d}{t} \\ d=s\cdot t \\ d=2\frac{1}{9}\cdot6 \\ d=\frac{18+1}{9}\cdot6=\frac{19}{9}\cdot6 \\ d=\frac{114}{9}=\frac{38}{3} \\ d=12\frac{2}{3} \end{gathered}[/tex]Therefore, the answer is the third option 12 2/3 miles
4. The pair of events that is non-mutually exclusive is A. Turning over an odd number and turning over an even number B. Turning over a prime number and turning over a perfect square C. Turning over a one-digit number and turning over a two-digit number D. Turning over a multiple of 2 and turning over a multiple of 7 5. A student draws one card at random from a standard deck of 52 playing cards. The probability that the card is a diamond or a face card is A. 0.058 B. 0.077 C. 0.423 D. 0.481 Use the following information to answer the next question. On any particular Saturday evening, the probability that Hannah will go 1 to the movies and go for a coffee is The probability that she will go
In one deck we have Spades, Clubs, Hearts, and Diamonds. Each one has 13 cards and 3 face cards. So the let's do this step by step. The probability to get a diamond card is:
[tex]P(diamond)\text{ = }\frac{13}{52}[/tex](13 diamond cards in a total of 52). Then the probability to get a face card is:
[tex]P(facecard)\text{ = }\frac{12}{52}[/tex](12 face cards in a total of 52). We have to sum these probabilities but also we have to subtract the possibilities that include a card that is a face card and diamond (because if we don't do that we are going to count these cards two times). This probability is:
[tex]P(DiamondandFaceCard)\text{ = }\frac{3}{52}[/tex](We have only 3 cards in the deck that are diamond and face cards). Therefore, the probability will be:
[tex]\text{Probability = P(diamond) + P(facecard) - P(Diamond and Face Card)}[/tex][tex]\text{Probability = }\frac{13}{52}\text{ + }\frac{12}{52}\text{ - }\frac{3}{52}[/tex][tex]\text{Probability = }0.423[/tex]Nanny using using an app that shows him how many kilometers he has to run to prepare for a Marathon. The app says here an 8.0 45 kilometer who wants to Post online how many miles away Danny ran blank miles.(one mile = 1.609 km)
The conversion for distance in kilometer to miles is as,
[tex]\begin{gathered} 1\text{ mile=1.609 km} \\ 1\text{ km=}\frac{1}{1.609}\text{ miles} \end{gathered}[/tex]Determine the number of miles in 8.045 km.
[tex]\begin{gathered} 8.045\text{ km=8.045}\cdot\frac{1}{1.609}\text{ miles} \\ =5\text{ miles} \end{gathered}[/tex]So Nanny ran 5 miles.
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. How many milliliters are in 1 quart? Label your answer to the hundredths place and in mL.
If we use RH as the base of this triangle, the height is ___ units.
ANSWER
[tex]6\text{ units}[/tex]EXPLANATION
To find the height of the triangle, using RH as the base, we simply have to find the vertical distance between the base and the top of the triangle.
To do that, find the difference between the y-coordinates of the top and the bottom of the triangle.
That is:
[tex]\begin{gathered} 8-2 \\ 6\text{ units} \end{gathered}[/tex]The height of the triangle is 6 units.
select the point(s) of the x intercept of the function shown below
ANSWER:
(-1, 0) and (3, 0)
STEP-BY-STEP EXPLANATION:
The x-intercept is the points where the graph crosses the x-axis, we can calculate it graphically like this:
A rectangle's length is 6 inches greater than its width. If the perimeter of the rectangle is 36 inches, find the length.
We will have the following:
First, we are given the following expressions for the rectangle's length and width respectively:
[tex]l=w+6[/tex]&
[tex]w=w[/tex]Now, we calculate the length and width using the perimeter:
[tex]P=2(l+w)\Rightarrow P=2(w+6+w)\Rightarrow P=2(2w+6)\Rightarrow P=4(w+3)[/tex]So:
[tex]36=4(w+3)\Rightarrow w+3=9\Rightarrow w=6[/tex]Then:
[tex]l=(6)+6\Rightarrow l=12[/tex]So, the measurements of the length and the width are respectively 12 units and 6 units.
Question 11
11 of 12
Which choice shows 13*07*4) correctly rewritten using the associative property and
then correctly simplified?
O (1347)*4=91*4=364
O 13*(4*7)=13*28=364
o 13*4*7=52*7=364
O (13*74)=962
Question ID: 116141
Submit
The associative property states that the way the factors are grouped in a multiplication does not change the result.
Grouping 7 and 4
13 * (4*7) = 13 *(28 ) = 364
13 and 7
(13*7)*4 = 91*4= 364
13 and 4
(13*4)*7 = 52*7 = 364
So, the correct options are a and b ( the first 2 options)
Question 8 of 10What should you multiply the first equation (top equation) by in order toeliminate the variable x when the two equations are added together?(3x-y-14-12x+y - 7dar hereISUBMIT
You can multiply the first equation by 4:
3x - y = 1 (*4)
12x-4y=4
Adding both equations:
12x - 4y = 4
+
-12x + y = 7
__________
0x - 3y = 11
so, you eliminate the X.
In order to eliminate the variable x when the two equations are added together, we needed to multiply the first equation by 4.
To eliminate the variable x when adding the two equations:
First, let's write the equations in a form where the x and y terms have opposite coefficients:
3x - y = 1 (Equation 1)
-12x + y = 7 (Equation 2)
To eliminate the x term, we can multiply Equation 1 by 4:
4 (3x - y) = 4 × 1
12x - 4y = 4 (Equation 3)
Now, we can add Equation 2 and Equation 3 together:
(-12x + y) + (12x - 4y) = 7 + 4
-12x + 12x + y - 4y = 11x - 3y = 11
The x term has been eliminated, and we are left with the equation 11x - 3y = 11.
To learn more about the system of equations;
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Which statement describes the product of the expression 5 x 1/2?A, It is less than 1/2B. It is greater than %. C. It is between 5 and 6. D. It is between 1/2 and 5.
we have the expression
[tex]5\cdot\frac{1}{2}=\frac{5}{2}[/tex]so
Verify each statement
A, It is less than 1/2 -----> is not true
B. It is greater than 5 ----> is not true
C. It is between 5 and 6 ----> is not true
D. It is between 1/2 and 5 ----> is true
because
1/2 < 5/2 < 5
therefore
The answer is option D
solve Equation: 4(x-6)=76
We have the next equation
[tex]4(x-6)=76[/tex][tex]\begin{gathered} x-6=\frac{76}{4} \\ x-6=19 \\ x=19+6 \\ x=25 \end{gathered}[/tex]Which set of graphs can be used to find the solution to the equation?
Given
The inequality,
[tex]3e^x>-\frac{1}{2}x[/tex]To find:
Which set of graphs can be used to find the solution to the equation?
Explanation:
It is given that,
[tex]3e^x>-\frac{1}{2}x[/tex]That implies,
The graph representing 3e^x is,
Also, the graph representing y> - ( 1/2) x is,
By combining these two we get,
[tex]3e^x>-\frac{1}{2}x[/tex]3.2= -4w+9.6 Solve for w
The given expression is,
[tex]3.2=-4w+9.6[/tex]On solving we have,
[tex]\begin{gathered} 4w=9.6-3.2=6.4 \\ w=\frac{6.4}{4}=1.6 \end{gathered}[/tex]Thus, the value of w
The dollar value v(s) of a certain car model that is t years old is given by» (t) = 25.900(0,92)Find the initial value of the car and the value after 12 years.Round your answers to the nearest dollar as necessary.Initial value:Value after 12 years.sx 5 ?
we have the following:
[tex]\begin{gathered} v(t)=25900\cdot(0.92)^t \\ v(0)=25900\cdot(0.92)^0=25900\cdot1=25900 \\ v(12)=25900\cdot(0.92)^{12}=25900\cdot0.3676=9522.56 \end{gathered}[/tex]therefore, tue intial value is 25900 and value after 12 yeras is 9523
Two Step problem:STEP 1: 7x^2 = -4using the standard form ax^2 +bx + c =0 of the given quadratic equation, factor the left hand side of the equation into two linear factors. STEP 2: 7x^2 = -4xsolve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. PICTURE OF ANSWER BOX ATTACHED: is for step #2
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
Step 1)
1) Let's factor that incomplete quadratic equation (since c=0):
7x² = -4x Add 4x to both sides
7x² + 4x = 0 Place outside the parenthese the common factor: x
x(7x+4) = 0
Step 2)
Now we can solve that:
x(7x+4)=0 Which number multiplied by x yields 0?
Then we can state that x_1 = 0
Solving that Linear Factor:
(7x +4) = 0 Removing the Parentheses
7x +4 = 0 Subtract 4 from both sides
7x = -4 Divide both sides by 7
x = -4/7
3) Hence, the answers are:
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
Identify which of the following graphs is the graph of two equivalent vectors.
By definition, two vector are equivalent when they have the same length, and they point in the same direction. Any two or more vectors will be equal if they are collinear, codirected, and have the same magnitude.
30.4. The figure below is going to be enlarged so that the area of the new, similar shape will be 400 cm?. What will the perimeter of the new, enlarged shape be?5 cm24. Perimeter of enlarged shape=cmicm10 cmArea = 100 cm2
Q. 4:
We are asked to find the perimeter of the enlarged shape.
The perimeter of the enlarged shape can be found by multiplying the scale factor with the perimeter of the original shape.
The scale factor is the ratio of the area of the enlarged shape to the area of the original shape.
[tex]SF=\frac{400\;cm^2}{100\;cm^2}=4[/tex]So, the scale factor is 4.
The perimeter of the original shape can be found by adding all the side lengths.
[tex]P=5+4+10+6+3+2=25\;cm[/tex]So, the perimeter of the original shape is 25 cm
Finally, the perimeter of the enlarged shape is
[tex]P=4\times25=100\;cm[/tex]Therefore, the perimeter of the enlarged shape is 100 cm
A gift box for a shirt has a length of 45 centimeters, a width of 30 centimeters, anda height of 8 centimeters. Find the surface area of the gift box
The main values in order to find the surface are the width and the length, therefore, the surface will be the product between them
[tex]45cm\times30cm=1350cm^2[/tex]Because the box cover from a gift box depends on the width and length, the surface area is 1350cm^2.
4. Look at the figures below.How was each point of Polygon ABCDE shifted to get Polygon BCDE?A right I unit and down 4 unitsBright I unit and down 1 unitC. left 1 unit and up 4 unitsD. left I unit and up 1 unitTi
Given a polygon ABCDE with the coordinates
[tex]A(-7,2),B(-8,4),C(-6,5),D(-5,6),E(-5,3)[/tex]The image of the polygon has vertices A'B'C'D'E' with coordinates
[tex]A^{\prime}(-6,-2),B^{\prime}(-7,0),C^{\prime}(-5,1),D^{\prime}(-4,2),E^{\prime}(-4,-1)[/tex]The transformation rule as observed from the image is
[tex](x,y)\Rightarrow(x+1,y-4)[/tex]Hence, the polygon has been shifted to the right by 1 unit and down by 4 units
Option A is the right answer
What is the 6th term in the geometric sequence described by this explicitformula?an = 500. (0.5)(n-1) choose one A. 1250B. 7.8125C. 15.625OD. 12,500
a6=?
[tex]a_6=500\times0.5\times(6-1)[/tex][tex]a_6=250\times5=1250[/tex]option A
If the probability of an event is what is the probability of the event not happening?20/69Write your answer as a simplified fraction.
If an event has a probability P of happening, then there is a probability of (1-P) of the event not happening.
In this case the probability of the event is p=20/69.
Then, the probability of the event not happening is:
[tex]P(\text{not happening})=1-p=1-\frac{20}{69}=\frac{69-20}{69}=\frac{49}{69}[/tex]Answer: the probability of the event not happening is 49/69.
compare a=0.432, b=0.437
So we need to compare two numbers. This means telling which is smaller and which is greater or if they are equal. In this case we have decimal numbers but it's more comfortable to work with integers so I'm going to multiply both by the same number in order to make them integers:
[tex]\begin{gathered} A=0.432\cdot1000=432 \\ B=0.437\cdot1000=437 \end{gathered}[/tex]Since both a and b where multiplied by the same number then the result of the comparison between A and B is the same as that between a and b. So we have 432 and 437. Let's make a substraction:
[tex]A-B=432-437=-5[/tex]The result is a negative number which means that:
[tex]A-B<0[/tex]Then we add B at both sides of this inequality:
[tex]\begin{gathered} A-B+B<0+B \\ AAs I said before the comparison between A and B is the same as that between a and b which means that:[tex]aAnd that last inequality is the answer. A scuba diver is swimming at a depth of 70 feet .He descended at a rate of 5 feet every 12 seconds.At this rate ,how many seconds did it take for the diver to reach the depth of 70 feet?
Can you please help me out with a question
ANSWER:
[tex]\text{center}=(\frac{3}{2},-\frac{1}{2})[/tex]STEP-BY-STEP EXPLANATION:
The center of the circle would be the mean value between the end points, and we can calculate it like this:
[tex]\begin{gathered} (M_1,M_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{replacing} \\ (M_1,M_2)=(\frac{-2+5_{}}{2},\frac{-4+3_{}}{2}) \\ (M_1,M_2)=(\frac{3_{}}{2},-\frac{1_{}}{2}) \end{gathered}[/tex]