The calculation of the mean shows that Jamie should not lose her job as she was faster after the talk from the boss.
How to calculate the mean?The mean of the travel time in the first scenario will be:
= (18, 20, 22, 27, 16, 23, 25,26, 19, 28)/10
= 224/10
= 22.4
She she shows consistency, the mean will be:
= (22, 20, 22, 24, 24, 23, 25, 21, 19, 21)/10
= 221/10
= 22.1
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- Write the inequality that shows how much money you can spend on the booth.
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if you have $1000 and need to buy 10 chairs worth $5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:
x + 10(5) ≤ 1000
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.
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(c) If f(x) = a^x , then show that f(m +n + p) = f(m). f(x). f(p)
[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]
What is the value of x in the equation 1/5x-2/3y = 30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
Given equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]
Steps:
1. Substitute 15 as the value of y in the equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]
2. Add 10 to both sides:
[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]
3. Multiply both sides by 5 to isolate x:
[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]
4. Check your work:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]
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Hey there!
Answer :[tex] \boxed{\bold{\green{ x = 200}}} [/tex]
[tex] \\ [/tex]
Explanation:Given expression :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]
1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
[tex] \\ [/tex]
2) Solve for x :
[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
⇢Add 10 to both sides of the equation :
[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
⇢Multiply both sides of the equation by 5:
[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]
[tex] \\ [/tex]
3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :
[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]
[tex] \\ \\ [/tex]
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The length of a reclangle can be represented by the expression 2x - 1. The width of the same rectangle can be represented by the expression x^2 - x + 3. Which of the following expressions can represent the area of the rectangle?
Answer:
2x^3 - 3x^2 + 7x - 3
Step-by-step explanation:
Area = length * width
= (2x - 1)(x^2 - x + 3)
= 2x(x^2 - x + 3) - 1(x^2 - x + 3)
= 2x^3 - 2x^2 + 6x - x^2 + x - 3
= 2x^3 - 3x^2 + 7x - 3
find slope of a straight line if both intercept are equal
Answer:
-1
Step-by-step explanation:
Let the points be (0, a) and (a, 0) (As it mentions the intercepts are equal)
==============================================================
Applying slope formula :
⇒ m = 0 - a / a - 0
⇒ m = -a/a
⇒ m = -1
Pre Calc question, thanks for the help! Question linked in photo below.
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{0} + 3 = 3[/tex]
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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Need help with this question!! ASAP!! Will give brainliest!!!!
Answer: x = log₃₇(12)
Step - by - step explanation:
1. Remove the variable from the exponent using logarithms
37^x=12
Take the common logarithm of both sides of the equation:
log₁₀(37^x)=log₁₀12)
Use the log rule: log_a(x^y)=y*log_a(x) to move the exponent outside the logarithm:
x*log₁₀(37)=log₁₀(12)
2. Isolate the x-variable
x*log₁₀(37)=log₁₀(12)
Divide both sides of the equation log₁₀(37) by:
x = log₁₀(12) / log₁₀(37)
Use the formula [tex]log_{b}(x)/log_{b}(a) = log_{a} (x)[/tex]
to combine the logarithms into one:
x=log₃₇(12)
Decimal form:
x=0.6881648129099501
Hope this helps!
Solve for the h in the triangle below. Round to the nearest tenth. 90⁰ 6.0 Oh-13.3 Oh 5.5 Oh 8.0 53%
Answer:
h=8.0
Step-by-step explanation:
law of sines
sinA/a=sinB/b
b/a=sinB/sinA
b = a times sinB/sinA
b = 10 times sin53/sin90
on a calculator type sin53 in degrees
b = 10 times 0.7986/1
b = 7.986
Equation of the circle is x^2 +(y-10)^2=16. The radius of the circle is___units. The center of the circle is at ___
Answer:
Radius=4 units
Centre= (0,-10)
Step-by-step explanation:
Given equation of circle is x^2 +(y-10)^2=16
Comparing it with (x-h)^2 +(y-k)^2 = r^2 ,we get,
r=4
Since, centre of a circle=(h,k)=(0,-10)
Answer:
Center (0;10) Radius= 4. Make me brainliest? :(
Step-by-step explanation:
[tex](x + 0)^{2} + (y - 10)^{2} = 16 \\ center(0.10) \\ radius = \sqrt{16} = 4[/tex]
Charlotte recorded the number of minutes she spent exercising in the past ten days: 12, 4, 5, 6, 8, 7, 9, 8, 2, 1. Find the median of the data.
Answer:
6.5
Step-by-step explanation:
Median is always the middle number of the set of data, so lets re order the numbers least to greatest
1,2,4,5,6,7,8,8,9,12
Since there's an even amount there wont be an exact middle number, however we know its in-between 6 and 7. So we can do 6+7 = 13 and then 13/2 = 6.5 to get the middle number or median.
This table shows the music preferences in 14- to 19-year-olds. A Circle Graph was made using this data and presented at a conference.
What could make people at the conference draw wrong conclusions from this Circle Graph?
A. The Country section has the smallest area.
B. The Rap section covers the largest area.
C. The Alternative section is larger than the rock and roll section.
D. The Classical section is not included in the Circle Graph.
The wrong conclusions that can be drawn from the circle graph are:
The Country section has the smallest area.
The Classical section is not included in the Circle Graph.
What is a circle graph?A circle graph is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees
In the circle graph, the country section has a percentage of 10% while the classical section has a percentage of 2%.
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Answer:
the answer is D
Step-by-step explanation:
look at the table there are 5 music genres but there's only 4 on the circle graph.
Find Measure of angle B (m18. a = 7 m, b = 5 m, m∠A = 45°
Answer:
30.34 degree
Step-by-step explanation:
Apply sine formula
[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]
[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]
->simplify
[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]
you will get
[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]
which
sin b is about 0.50507
[tex]sin^{-1}\left(0.50507\right)[/tex]
->arc sine in degree mode
the answer is 30.34
A comparson of two or more quantities of the same kind is called a
pls help me answer thiss. I really really need help! thank u
Answer:
see explanation
Step-by-step explanation:
the centroid is where the medians intersect.
On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.
(3)
GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7
CF = CG + GF = 14 + 7 = 21
(4)
GD = [tex]\frac{1}{3}[/tex] AD = [tex]\frac{1}{3}[/tex] × 45 = 15
AG = 2 × GD = 2 × 15 = 30
(5)
GE = 2 × BG , that is
9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
6x - 5y = 8
-12x + 2y = 0
Answer:
the answer is in picture
Step-by-step explanation:
hope it will help you
If $3840 is deposited into a bank account at a 5% interest rate how long will it take the account to make $960 in interest?
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
Answer:
132°
Step-by-step explanation:
We use the circle theorem which states that :
Opposite angles in a cyclic quadrilateral add up to 180 .
Now we know that angles ADC and ABC add up to 180. So :
We make an equation and solve for x :
x+(3x-12) = 180
4x-12 = 180
4x = 192
x = 48
Now we substitute the value of x into Angle B :
3(48) -12 =
144 - 12 = 132
Angle B = 132 °
Hope this helped and have a good day
WILL GIVE 100 POINTS PLS HELP RN EVEN IF ITS JUST A FEW
In order to determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of student population enrolled in the programs.
Popular Majors Percent of Student Body
Biology 8%
Business Marketing 20%
Communications/Journali 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
The university’s enrollment is expected to reach at least 20,000 students for the fall semester.
1. The minimum number of students who are expected to be working towards a Social Sciences degree is ???
2. The university requires that any student who is studying Visual and Performing Arts or Communications Journalism must perform in one of the student productions before graduation. At least ??? of the 20,000 students will be performing in the university’s student productions before graduation.
3.
In the fall semester, ???% of the student population will be enrolled in a degree program not listed as one of the university’s most popular.
The most popular degree offered at Arizona State University is ???
4. The most popular degree offered at Arizona State University is ???
5. For the fall semester, the university should expect that ??? students will enroll in one of the two most popular degree programs.
1. 20,000×10%=2,000
2. 20,000×14%=2,800
3. 20,000×5%=1,000
4. Business Marketing
5. 20,000×30%=6,000
5 feet to 31 inches write the ratio of the first measurement to the second measurement compare in inches
Answer:
60:31
Step-by-step explanation:
The table below represents the closing prices of stock ABC for the last five
days. Using your calculator, what is the equation of linear regression that fits
these data?
Day
Value
1
20.71
2
19.69
3
19.61
4
19.64
5
19.26
OA. y = 0.289x + 21.459
OB. y=-0.311x + 19.213
O C. y=-0.295x+20.667
D. y=-0.272x+22.319
Using a calculator, it is found that the equation of linear regression that fits the data is given by:
C. y=-0.295x+20.667
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:
Doing this, the equation is:
y = -0.295x + 20.667.
Hence option C is correct.
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Looking for the answer to this question
Answer:
Option A: Linear Regression
Step-by-step explanation:
The sale values do not increase in a quadratic or exponential function.
At central high school there are 398 sophomores who do not own a car and 29 who do there are 64 juniors who own a car and 339 who do not there are 123 seniors who own a car compared to 239 who do not complete the two way table to display these data
The proportion of sophomores that do not own a car is equal to 0.93.
What is ratio?Ratio is a mathematical expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
The proportion of sophomores that do not own a car is given by:
Number of sophomores that do not own a car = 398.Total number of sophomores = 427Therefore, proportion = 398/427 = 0.93.
The proportion of all students who are seniors who own cars is given by:
Number of seniors who own cars = 123Total number of students = 1192Therefore, proportion = 123/1192 = 0.10.
The proportion of non-car owners who are juniors is given by:
Number of juniors who are non-car owners = 339Total number of students that do not own a car = 976.Therefore, proportion = 339/976 = 0.35.
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Complete Question:
At Central High School, there are 398 sophomores who do not own a car and 29 who do. There are 64 juniors who own a car and 339 who do not. There are 123 seniors who own a car, compared to 239 who do not. The above is a two-way table depicting this situation. Complete the following statements below by finding the ratio, then converting to a decimal. Round to the nearest hundredth.
The proportion of sophomores that do not own a car is?
The proportion of all students who are seniors who own cars is?
The proportion of non-car owners who are juniors is?
The equation of line A is y = 5 - 2x Line B is parallel to line A. Line B passes through the point (-3,7)
Work out the coordinates of the point where line B intersects the x-axis.
Answer:
The answer is (0.5, 0)
Step-by-step explanation:
A rectangle is divided into exactly 20 congruent squares. Then these squares are lined up in a single row extending 36 inches (3 feet). What was the area of the rectangle?
The area of the rectangle is 64.8 square .inch
What is a Rectangle ?A rectangle is a polygon with four sides , opposite sides are parallel and equal.
It is given that
A rectangle is divided into exactly 20 congruent squares
If they are lined up the Length is 36 inches
Therefore the length of each square or the side of the square = 36/20
= 1.8 inch
The area of the rectangle will be
20* Side of square * Side of square
=20*1.8*1.8
= 64.8 square inch
The area of the rectangle is 64.8 square .inch
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Suzie's Slushes has increasing profits each week during the hot summer months. Suzie finds that each week during the summer her profits increase by 30% over what they were the previous week. In her first week of business, her profits were $300. How much money will she make in all over 4 weeks
The amount of money that Suzie will make over the four weeks is; $1856
How to find amount of profit made?
Suzie will make a profit of:
The first week = $300
The second week = (300 * 30%) + 300 = $390
The third week = 390 * (1430%) = $507
The fourth week: 507 × (1430%) = $659.1
Thus, Sum of profit = $300 + $390 + $507 + $659.1
Sum of Profit = $1856.1 ≈ $1856
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A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 12 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The correct true statement is: b. The swimmer comes back up 9 seconds after the timer was started.
The swimmer's maximum depth (in feet)Given:
h(t)=t^2−12t+27
Let velocity of the function= 0
h(t) = 2t - 12
0 = 2t - 12
2t = 12
Divide both side by 2t
t=12/2
t = 6secs
Substitution
h(6) = 6²-12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
The correct statement is b.
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Dina is shipping a wall map to a collector. When the map is rolled up, it measures
7 ft long. She will use a box that is a right rectangular prism with a base that is 3 ft
by 3 ft. Which whole number could be the shortest height of the box that will hold
the map?
A 4 ft
B 5 ft
C 6 ft
D 7 ft
The shortest height of the box that will hold the map is 6 ft option (C) is correct.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have:
Dina is shipping a wall map to a collector. When the map is rolled up, it measures.
From the figure we can apply the Pythagoras theorem to find the length BA:
BA² = 3² + 3²
BA = √18
Again applying Pythagoras theorem:
The height
AD² = 7² - (√18)²
AD² = 31
AD = √31 ft = 5.56 ft ≈ 6 ft
Thus, the shortest height of the box that will hold the map is 6 ft option (C) is correct.
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Rational and irrational numbers
Answer:
Rational numbers is a ratio (i.e., P/Q and Q≠0)
Irrational numbers cannot be expressed as a fraction.
so a
Rational numbers can show a Fraction
Irrational numbers can not show a Fraction
Hope This Helped
Answer:
Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.
Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.
6
the incomplete pictogram shows information about the number of eggs sold
shop on monday.
monday
tuesday
wednesday
on monday the shop sold 18 eggs.
on tuesday the shop sold 24 eggs.
on wednesday the shop sold 27 eggs.
use this information
The number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
Given on Monday the shop sold 18 eggs. Therefore, each quarter of the circle represents 3 eggs.
Hence, the number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.
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the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
How to determine the radius of the smaller circle
In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:
[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]
2 · r² = (9-r)²
2 · r² = 81 - 18 · r + r²
r² + 18 · r - 81 = 0
The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
Remark
The image is missing and is thus included in the figure attached below.
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