Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...
Step-by-step explanation:
The composition of rigid motions T (-20,-6) •T (19,23 describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north. First the limousine drives (Type whole numbers.) block(s) east and block(s) north, and then it drives block(s) east and block(s) south.
You have the following rigid motion:
[tex]T_{<-20,-6>}T_{<19,23>}[/tex]The previous transformation means that the limousine was translated 20 units to the west and 6 units downward (south), next, the limousine was translated 19 units to the east and 23 units upward (north).
Hence, the limousine drives 20 blocks to the east and 6 blocks to south, and then it drives 19 block to the east and 23 blocks to north.
Laura, Sam, and Miguel served a total of 121 orders Monday at the school cafeteria, Miguel served 7 fewer orders than Laura. Sam served 4 times as manyorders as Miguel. How many orders did they each serve?Number of orders Laura served:Number of orders Sam served:Number of orders Miguel served:
Let L, S, and M, denote the number of orders served by Laura, Sam, and Mighuel, respectively, on Monday at the school cafeteria.
Given that the total 121 orders were served,
[tex]L+S+M=121\ldots(1)[/tex]Given that Miguel served 7 fewer orders than Laura,
[tex]\begin{gathered} M=L-7 \\ L=M+7 \end{gathered}[/tex]Given that Sam served 4 times as many orders as Miguel,
[tex]\begin{gathered} S=4\cdot M \\ S=4M \end{gathered}[/tex]Substitute the values of 'L' and 'S' in equation (1),
[tex](M+7)+(4M)+M=121[/tex]Simplify the above expression,
[tex]\begin{gathered} M+7+4M+M=121 \\ 6M+7=121 \\ 6M=121-7 \\ M=\frac{121-7}{6} \\ M=19 \end{gathered}[/tex]The corresponding values of L and S will be,
[tex]\begin{gathered} L=19+7=26 \\ S=4\cdot19=76 \end{gathered}[/tex]Thus, Laura served 26 orders, Sam served 76 orders, while MIguel served 19 orders on Monday at the school cafeteria.
Suppose you know students at school are, on average, 68 inches tall with a standard deviation of 4 inches. If you sample 36 students, what is the probability their average height is more than 70 inches?
Answer:
0.135% or 0.00135
Explanation:
• The population mean height = 68 inches
,• The population standard deviation = 4 inches
,• Sample Size, n = 36
First, find the sample standard deviation:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{4}{\sqrt{36}}=\frac{4}{6}=\frac{2}{3}[/tex]Next, for X=70, find the z-score:
[tex]\begin{gathered} z-score=\frac{X-\mu}{\sigma_x} \\ z=\frac{70-68}{2\/3}=\frac{2}{2\/3}=3 \end{gathered}[/tex]Since we are looking for the probability that their average height is more than 70 inches, we need to find:
• P(X>70)=P(z>3)
Using the z-score table:
[tex]P(z>3)=0.0013499[/tex]The probability that their average height is more than 70 inches is 0.135%.
Can someone help me with this?
x to the zeroth power - 3x +5
Question 7(Multiple Choice Worth 3 points)(05.04 LC)triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle RIf ∠R measures 18°, q equals 9.5, and p equals 6.0, then which length can be found using the Law of Cosines? p q RQ PQ
Answer
PQ
Explanation
It must be PQ because we have the measure of the other two sides and the angle opposite it.
Together, Katya and Mimi have 480 pennies in their piggy banks. After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left. How many pennies did they lose altogether?
The number of pennies they lose altogether is 288 pennies.
How to find the number of pennies they lost together?Together, Katya and Mimi have 480 pennies in their piggy banks.
Therefore, there total amount of pennies is 480.
After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.
Therefore,
let
x = number of pennies Katya have
y = number of pennies Mimi have
Hence,
x + y = 480
x = 480
Katya pennies left = x - 1 / 2x = 1 / 2x
Mimi pennies left = y - 2 / 3 y = 1 / 3 y
1 / 2 x = 1 / 3 y
2y = 3x
y = 3 / 2 x
Substitute the value in equation(i)
x + 3 / 2 x = 480
2.5x = 480
x = 480 / 2.5
x = 192
Therefore,
192 + y = 480
y = 480 - 192
y = 288
The number of pennies they loose can be calculated as follows;
Katya losses = 1 / 2 × 192 = 96Mimi losses = 2 / 3 × 288 = 192Therefore, they lost 96 + 192 = 288 pennies altogether.
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During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)
Answer:
11 percent
Step-by-step explanation:
No idea to explain
Elisa has 24 black and white photographs and 72 photographs that are in color. She is arranging the photographs in an album and wants to contain the same combination of color and black and white photographs. What is the greatest number of pages elisa can fill with photographs
Make the following conversions. Round to 2 decimal places, where necessary.8 feet 9 inches toa. Inches: in.b. Feet: ft
Given the measurement
[tex]8feet\text{ 9inches}[/tex]a) To convert to inches,
Where
[tex]1ft=12in[/tex][tex]8ft\text{ to inches}=8\times12=96[/tex]8 feet 9 inches in inches is
[tex]\begin{gathered} 8ft\text{ 9in}=8ft+9in=96+9=105in \\ 8ft\text{ 9in}=105in \end{gathered}[/tex]Hence, 8 feet 9 inches in inches is 105in
b) To convert to feet,
Where
[tex]1in=\frac{1}{12}ft[/tex][tex]9in\text{ to f}eet=9\times\frac{1}{12}=\frac{9}{12}=0.75ft[/tex]8 feet 9 inches in feet is
[tex]8ft\text{ 9in}=8ft+9in=8+0.75=8.75ft[/tex]Hence, 8 feet 9 inches in feet is 8.75ft
Hi, can you help me answer this question please, thank you!
The sample size given in the question is
[tex]n=37[/tex]The mean weight is
[tex]\bar{x}=50[/tex]The standard deviation is
[tex]\sigma=8.4[/tex]The margin of error is calculated using the formula below
[tex]\text{MOE = Z-score(90\% C.I)}\times\frac{\sigma}{\sqrt[]{n}}[/tex]Using the Z-score table, the Z-score for the 90% confidence interval is
[tex]=1.645[/tex]By substituting the values in the formula above, we will have
[tex]\begin{gathered} \text{MOE = Z-score(90\% C.I)}\times\frac{\sigma}{\sqrt[]{n}} \\ \text{Margin of error(MOE)} \\ =1.645\times\frac{8.4}{\sqrt[]{37}} \\ =\frac{13.818}{\sqrt[]{37}} \\ =\pm2.272\text{ounces} \end{gathered}[/tex]Hence,
The final answer is = ±2.272 ounces
It takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 10 inches wide, and 14 inchestall. How long will it take the same hose to fill an aquarium measuring 23 inches by 25 inches by 26inches?minutesEnter an integer or decimal number [more..]Round your answer to the nearest minuteSubmit
Answer:
[tex]40\text{ minutes}[/tex]Explanation:
Firstly, we have to calculate the rate at which the hose works
We can get that by dividing the volume of the first aquarium by the time taken to fill it
The volume of the first aquarium can be calculated using the formula:
[tex]V\text{ = L}\times B\times H[/tex]Where:
L is the length of the aquarium
B is its width
H is its height
The volume of the first aquarium is thus:
[tex]V\text{ = 8}\times10\times14\text{ = 1120 in}^3[/tex]We have the filling rate as:
[tex]\frac{1120}{3}\text{ in}^3\text{ per minute}[/tex]Now, let us get the volume of the second aquarium
We use the same formula as the first
We have the volume as:
[tex]23\times25\times26\text{ = 14,950 in}^3[/tex]Now, to get the time taken, we divide the volume of the second aquarium by the rate of the first
Mathematically, we have that as:
[tex]14950\text{ }\times\frac{3}{1120}\text{ = 40 minutes approximately}[/tex]Persevere with Problems Analyze how the circumference of a circle would change if the diameter was doubled. Provide an example to support your explanation.
Circumference of a circle . Girth
Circumference C= π•D
Then if D'=2D
New Circumference C'= π•2D = 2•π•D
Circumference is doubled, if diameter is doubled
EXAMPLE
Suppose D= 5 cm
Then C= π•5 = 15.70
If D'= 2•5=10 cm
Then C'= π•10= 31.415
Now divide C'/C = 31.415/15.70 = 2.00
the value of square root (8/64)³
The expression is
[tex]\begin{gathered} (\sqrt[]{\frac{8}{64}})^3 \\ By\text{ simplifying, we have} \\ (\sqrt[]{\frac{1}{8}})^3 \\ =\text{ (}\frac{1}{8})^{\frac{3}{2}} \\ 0.0442 \end{gathered}[/tex]Reflected over the x-axis , horizontal shrink of 1/2, translated 7 down.
Given:
Reflected over the x-axis, horizontal shrink of 1/2, translated 7 down.
The parent function is y=|x|.
[tex]\begin{gathered} \text{reflected over x-axis=-f(x)} \\ \text{horizontal shrink=f(}\frac{x}{b}\text{)} \\ \text{translation to the down=f(x)-d} \end{gathered}[/tex]The function becomes,
[tex]y=-|2x|-7[/tex]Answer:
[tex]y=-|2x|-7[/tex]Hi there, I need help with this question. Thank you in advance!
For the data given, we have 24 entries in all.
They are :
75, 36, 80, 49, 24, 61, 34, 39, 30, 76, 44, 44, 40, 35, 21, 89, 34, 70, 79, 65, 66, 53, 99, 11
(1) Minimum refers to the lowest data in the table. we can see out of all the data in the table, the lowest is 11. Therefore,
Min = 11
(2) Maximum refers to the highest data in the table.
The highest is 99.
Therefore,
Max = 99
(3) Range is defined as highest data minus lowest data
Range = 99 - 11
Range = 88
(4) Mean:
[tex]\begin{gathered} \text{ Mean =}\frac{\text{ sum of the data}}{total\text{ count}} \\ \operatorname{mean}\text{ = }\frac{75+36+80+49+24+61+34+39+30+76+44+44+40+35+21+89+34+70+79+65+66+53+99+11}{24} \\ \\ \text{Mean = }\frac{1254}{24} \\ =52.25 \end{gathered}[/tex]Therefore,
Mean = 52.25
(5) Standard deviation:
The steps to calculate the standard deviation in shown in the picture below.
The standard deviation = 22.8386..
To 2 decimal places, we have 22.84
Therefore,
Standard deviation = 22.84
1) What is the surface area of this Cylinder: height of 9cm and a radius of 7cm. 1) Use 3.14 and round your a 9 cm
EXPLANATION
This is a cylinder with a height of 9 cm and a radius of 7cm.
The Area of a cylinder is given by the following expression:
Area= 2xπxr ² + 2xπxrxh
As r=7cm and h=9cm, replacing terms:
Area = 2xπx(7) ² + 2xπx7x9
Multiplying numbers:
Area = 98xπ + 126xπ
Simplifying:
Area= 224xπ
Representing π as a number:
Area= 224 x 3.14= 703.36 cm^2
(4xy³y⁴)(5x²y) expand and simplify
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(4xy³y⁴)(5x²y)
Step 02:
[tex](4xy^3y^4)(5x^2y)=(4xy^7)(5x^2y)=20x^3y^8^{}[/tex]This is the solution.
[tex]20x^3y^8^{}[/tex]system of equationsb+c= -55b-c= 17
Let's solve the system of equations:
b + c = - 55
b - c = 17
Step 1: Let's isolate b on the first equation:
b + c = - 55
b = - 55 - c
Step 2: Let's solve for c on the second equation, substituting b:
b - c = 17
-55 - c - c = 17
-55 - 2c = 17
Adding 55 at both sides:
-2c - 55 + 55 = 17 + 55
-2c = 72
Dividing by - 2 at both sides:
-2c/-2 = 72/-2
c = -36
Step 3: Let's solve for b on the first equation, susbtituting c:
b + c = - 55
b + (-36) = - 55
b - 36 = - 55
Adding 36 at both sides:
b - 36 + 36 = - 55 + 36
I think you are ready to finish and calculate the value for b.
NEED HELP FAST!!
For ΔABC, m∠A = 41.3° and m∠B = 103.4°. Determine m∠C.
144.7°
72.35°
54.7°
35.3°
Answer: The answer is D. 35.3
Step-by-step explanation: Because the triangle has to add up to 180 and 41.3 + 103.4 = 144.7. Then you could either do 180-144.7 = 35.3 or you could add 144.7 + 35.3. Hope this helps
The value of angle C based on the information is A. 35.3°
How to calculate the angle?It's important to know that the total sum of angles in a triangle is 180°.
In this case, the following can be deduced:
Angle A = 41.3°
Angle B = 103.4°
Therefore, Angie C will be:
= Total angle - {Angle A + Angle B}
= 180° - (41.3° + 103.4°)
= 180° - 144.7°
= 35.3°
Therefore, the correct option is D.
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When you start your career, you decide to set aside $500 every quarter to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 10.0% compounded quarterly. Assuming this to be true, how much money will your account be worth after 25 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Given:
The principal amount = $500
Interest rate = 10% quarterly
Required:
Find the deposing amount after 25 years.
Explanation:
The amount formula when the interest is compounded quarterly is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r = interest rate
t = time period
n = The number of compounded times
The amount after 25 years is:
[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]Final Answer:
The amount after 25 years will be &5906.85
If three angles of a triangle are 2x°, 6x° and x°, find the size of largest angle.
Answer:
so the answer is 6x°which is equals to 120°
Step-by-step explanation:
2x°+6x°+x°=180(The sum of the interior angle of the triangle is 180°)
9x°=180°
9x°÷9=180°÷9
x=20°
2x°is equals to 2×20°=40°
6x° is equals to 6×20°=120°
x° is equals to x×20°=20°
what is 140% 150,000
140 % of 150,000
[tex]\begin{gathered} 140\text{ \%=}\frac{140}{100} \\ \frac{140}{100}\times150000=\frac{21000000}{100}=210,000 \end{gathered}[/tex]I need to the equation of a line as (-5,-3); slope = -3/5
To answer this question, we will use the following formula for the equation of a line that passes through (x₁,y₁), and has slope m:
[tex]y-y_1=m(x-x_1)\text{.}[/tex]Substituting (x₁,y₁)=(-5,-3) and m=-3/5 in the above formula we get:
[tex]y-(-3)=-\frac{3}{5}(x-(-5))\text{.}[/tex]Simplifying the above equation we get:
[tex]\begin{gathered} y+3=-\frac{3}{5}(x+5), \\ y+3=-\frac{3}{5}x-\frac{3}{5}5, \\ y+3=-\frac{3}{5}x-3, \\ y+3-3=-\frac{3}{5}x-3-3, \\ y=-\frac{3}{5}x-6. \end{gathered}[/tex]Answer:
[tex]y=-\frac{3}{5}x-6\text{.}[/tex]Solve the system of two equations in two variables.6x - 7y = 282x + 4y = -16
Answer:
Explanation:
Given the system of equations
[tex]\begin{gathered} 6x-7y=28 \\ 2x+4y=-16 \end{gathered}[/tex]We intend to use the elimination method to solve it.
• Multiply the first equation by 2
,• Multiply the second equation by 6
This gives us:
[tex]\begin{gathered} 12x-14y=56 \\ 12x+24y=-96 \end{gathered}[/tex]We eliminate x by subtracting.
[tex]undefined[/tex]If z = 30, use the following proportions to find the value of x. x : y = 3:9 and y : z = 6 : 20.
We are given the following proportions:
[tex]\begin{gathered} x:y=3:9 \\ y:z=6:20 \end{gathered}[/tex]The second proportion is equivalent to:
[tex]\frac{y}{z}=\frac{6}{20}[/tex]Now, we substitute the value of "z":
[tex]\frac{y}{30}=\frac{6}{20}[/tex]Now, we multiply both sides by 30:
[tex]y=30\times\frac{6}{20}[/tex]Solving the operation we get:
[tex]y=9[/tex]Now, since we have the value of "y" we can use the first proportion to get the value of "x":
[tex]x_:y=3:9[/tex]This is equivalent to:
[tex]\frac{x}{y}=\frac{3}{9}[/tex]Now, we substitute the value of "y":
[tex]\frac{x}{9}=\frac{3}{9}[/tex]Now, we multiply both sides by 9:
[tex]x=9\times\frac{3}{9}[/tex]Solving the operations:
[tex]x=3[/tex]Therefore, the value of "x" is 3.
A triangular pryamid is shown in the diagram. What is the volume of the triangular pyramid?
Given the following question:
[tex]\begin{gathered} V=\frac{1}{3}BH \\ B=\text{ Base Area} \\ A=\frac{1}{2}BH \\ B=7.8 \\ H=4 \\ A=\frac{1}{2}7.8(4) \\ 7.8\times4=31.2 \\ 31.2\div2=15.6 \\ A=15.6 \\ V=\frac{1}{3}BH \\ B=15.6 \\ H=4 \\ \frac{1}{3}15.6(4) \\ 15.6(4)=62.4 \\ 62.4\div3=20.8 \\ V=20.8 \end{gathered}[/tex]Volume is equal to 20.8 cubic centimeters.
Segment RS is translated by (x+1, y-2) and then reflected over the x-axis. The resulting segment R" S" has coordinates R" (7,3) and
S" (2,7). What are the coordinates of the segment RS?
can someone pls help meee
Answers:
R = (6, -1)
S = (1, -5)
==========================================================
Explanation:
R'' is located at (7,3)
Reflect this over the x axis to get R'(7,-3). We flip the sign of the y coordinate while keeping the x coordinate the same. The rule is [tex](x,y) \to (x,-y)[/tex]
Then we apply the inverse of (x+1, y-2) which is (x-1, y+2). Notice the sign flips.
Let's apply this inverse transformation to determine the coordinates of point R.
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(7,-3)\to(7-1,-3+2)\\\\(7,-3)\to(6,-1)\\\\[/tex]
Therefore, point R is located at (6, -1)
-------------------
Point S'' is at (2,7)
It reflects over the x axis to get to (2,-7)
Then we apply that inverse transformation to get
[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(2,-7)\to(2-1,-7+2)\\\\(2,-7)\to(1,-5)\\\\[/tex]
Point S would be located at (1, -5)
Area of a rectangle: A Solve for) Find l when A= 24 ft and u
The area of the rectangle is 24 ft^2
the width of the rectangle is w = 8 ft
The expression for the area of the rectangle is given as follows.
A = l * w
[tex]\begin{gathered} 24=l\times8 \\ l=\frac{24}{8}=3 \end{gathered}[/tex]The length is l = 3 ft.
[tex]l=\text{ 3 ft}[/tex]Which of the following is a solution to the equation 16=4x-4?
Given:
[tex]16=4x-4[/tex][tex]16=4x-4[/tex][tex]20=4x[/tex][tex]\frac{20}{4}=x[/tex][tex]5=x[/tex][tex]x=5[/tex]Therefore , 5 is the answer.
Answer:5 is the answer.
Step-by-step explanation:
Need Help Asaaaappp look at scrrenshot
PR = 32
Equation:
Perimeter = PR + RQ + QP
67 units = (4x) + (x + 2) + (3x + 1)
67 = 8x + 3
64 = 8x
x = 8 units
Substitute x:
PR = (4x) = 4 * 8 = 32 units
RQ = (x + 2) = 8 + 2 = 10 units
QP = (3x + 1) = 3 * 8 + 1 = 25 units
PR = 32
Equation:
Perimeter = PR + RQ + QP
67 units = (4x) + (x + 2) + (3x + 1)
67 = 8x + 3
64 = 8x
x = 8 units
Substitute x:
PR = (4x) = 4 * 8 = 32 units
RQ = (x + 2) = 8 + 2 = 10 units
QP = (3x + 1) = 3 * 8 + 1 = 25 units