Cost of lectures = $7.33 per hour
ExplanationLet [tex]e[/tex] the cost of the exam hours
Let [tex]w[/tex] be the cost of the workshop hours
Let [tex]l[/tex] be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
[tex]e=2w[/tex] equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
[tex]w=2l[/tex] equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
[tex]3e+24w+12l=528[/tex] equation (1)
Now, lets find the value of [tex]l[/tex]:
Step 1. Solve for [tex]l[/tex] in equation (3)
[tex]3e+24w+12l=528[/tex]
[tex]12l=528-3e-24w[/tex] equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
[tex]12l=528-3e-24w[/tex]
[tex]12l=528-3(2w)-24w[/tex]
[tex]12l=528-6w-24w[/tex]
[tex]12l=528-30w[/tex] equation (5)
Step 3. Replace equation (2) in equation (5) and solve for [tex]l[/tex]
[tex]12l=528-30w[/tex]
[tex]12l=528-30(2l)[/tex]
[tex]12l=528-60l[/tex]
[tex]72l=528[/tex]
[tex]l=\frac{528}{72}[/tex]
[tex]l=\frac{22}{3}[/tex]
[tex]l=7.33[/tex]
Cost of lectures = $7.33 per hour
what type of relationship does this pair of angles have?67 degrees and 23 degrees
67° and 23° are complementary angles.
67 + 23 = 90
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
We know that, a ray is a line that continues on forever inn one direction with a point at it's start.
here, we have,
67 degrees and 23 degrees
we know,
67 + 23 = 90
Hence, 67° and 23° are complementary angles.
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At the end of 2005, the national debt for the U.S. was about 10 trillion dollars, and the population of the U.S. was about 10 to the 8th power. About how much was the per capita (per person) debt?
Final answer:
To find the per capita debt in 2005, divide the national debt of $10 trillion by the U.S. population of 100 million. The per capita debt comes out to be approximately $100,000 per person.
Explanation:
To calculate the per capita debt, we need to divide the national debt by the population of the U.S. The question states that the national debt at the end of 2005 was about $10 trillion, and the population was about 10 to the 8th power (100,000,000). To find the per capita debt, we perform the following calculation:
Per Capita Debt = Total National Debt / Population
= $10,000,000,000,000 / 100,000,000
= $100,000
Thus, the per capita debt was approximately $100,000 per person at the end of 2005.
540 seconds how many minutes
a triangular pyramid has a volume of 840 cubic inches the triangular base has a base length of 20 inches and a height of 21 inches find the height of the pyramid
The required height of the pyramid is 6 inches.
Given that,
A triangular pyramid has a volume of 840 cubic inches a triangular base has a base length of 20 inches and a height of 21 inches find the height of the pyramid is to be determined.
What is volume?Volume is defined as the ratio of the mass of an object to its density. In other words, the Volume of the object is the product area of the cross-sectional profile and extruded height.
Here,
The base area of the triangle = 20 * 21 = 420 inches².
Volume of the triangular pyramid = 1 / 3 * base area * height
840 = 1 / 3 * 420 * height
840 / 140 = height
height = 6 inch.
Thus, the required height of the pyramid is 6 inches.
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Angles A, B, and C represent the three angles of triangle ABC. If the measure of angle A is (4x - 8)°, the measure of angle B is (5x+2)°, and the measure of angle C is (6x-9)°, what is the measure of angle B (in degrees)?
simplify 6x + 8 / 4x + 4
1 over 4a = 2 over 3. Which of the following equals a in this equation?
1/6
3/8
11/12
2 and 2/3
Answer:
2 and 2 over 3 is the Correct Answer
Step-by-step explanation:
I took the test and got the question wrong, I thought it was 3/8 but it wasnt, my test said the correct answer was 2 and 2 over 3 so I hope you get it right even though I didnt :)
The solution of the expression is,
⇒ a = 3 / 8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 1 over 4a = 2 over 3.
Now, We can simplify as;
⇒ `1 / 4a = 2 / 3
⇒ 3 = 2 x 4a
⇒ 3 = 8a
⇒ a = 3 / 8
Thus, The solution of the expression is,
⇒ a = 3 / 8
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Sarah multiplied 4.16 and 1.83, as shown. But she forgot to put a decimal point in the answer. Complete the sentence below.
Answer:
The decimal point should be placed between the digits 7 and 6 because the product should be greater than 4 × 1 and less than 5 × 2.
Step-by-step explanation:
anyone know the answer?
A. 41 Cu in
B. 83 Cu in
C. 124 Cu in
D. 166 Cu in
Water rushes over Niagara Falls at the rate of 180 million cubic feet every 30 mins. How much water goes over the falls in 1 min?
also, please tell me the steps to do it, instead of just the answer
Answer:
20 million cubic feet every 1 mins
Step-by-step explanation:
180÷3=60
60÷3=20
A store is selling candy for $6 for 12 bags how much will it cost if you need to have 110 bags
A contest on a game show receives -25 points for each wrong answer what integer represents the change in periods after three wrong answers
How would 5,608,912,013 be written in word form? A. five million, six hundred eight thousand, nine hundred twelve, thirteen B. five million, six hundred eighty-nine thousand, twelve hundred, thirteen C. five billion, six hundred eight million, nine hundred twelve thousand, thirteen D. five billion, six hundred eighteen million, nine hundred twelve thousand, thirteen
What is (-34) divided by (1.2) rounded to the nearest hundredth
Is 11 to 15 correct?
Rewrite the following equation in slope-intercept form. 17x − 7y = 16 Write your answer using integers, proper fractions, and improper fractions in simplest form.
The map At the right shows ELLies locker,her English class,and the cafeteria.is her locker closer to the English class or the cafeteria?
The locker is closer.
What is the area or perimeter for carpeting a floor?
The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet, while the perimeter refers to the total length around the edges of the floor.
Explanation:The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet. The perimeter, on the other hand, refers to the total length around the edges of the floor. The choice between calculating the area or perimeter for carpeting a floor depends on whether you need to determine how much carpet material is needed (area) or how much carpet edge is required (perimeter).
For example, if you want to calculate the area to determine the amount of carpet needed to cover the floor, you would measure the length and width of the floor and multiply them together. The resulting area would be in square units (such as square feet or square meters).
On the other hand, if you want to calculate the perimeter to determine how much carpet edge needs to be trimmed or finished, you would add up the lengths of all the sides of the floor. The resulting perimeter would be in linear units (such as feet or meters).
Question 10 please :(
find the sum
the answer is after the first one
The table shows the number of hours two groups of teens spent on science and math homework last week. Each group was made up of 10 teens. 13- to 14-year olds 10 9 11 8 10 10 2 7 8 12 15- to 16-year olds 12 10 8 11 12 12 6 4 4 10 Select from the drop-down menus to correctly complete each statement. The mean hours the groups of teens spent studying is , The range for the two groups of of teens is .
Answer: The mean hours the groups of teens spent studying is little bit greater for 15- to 16-year old teen or about same .
The range range for the two groups of of teens is greater for 13- to 14-year old teens.
Step-by-step explanation:
We know that the mean of a data is given by :-
[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Range = largest observation - least observation
From the given table :
The mean hours spent by 13- to 14-year olds is given by :-
[tex]\text{Mean}=\dfrac{87}{10}=8.7[/tex]
[tex]\text{Range=12-2=10}[/tex]
The mean hours spent by 15- to 16-year olds is given by :-
[tex]\text{Mean}=\dfrac{89}{10}=8.9[/tex]
[tex]\text{Range=12-4=8}[/tex]
The mean hours the groups of teens spent studying is little bit greater for 15- to 16-year old teen or can say about same.
The range range for the two groups of of teens is greater for 13- to 14-year old teens.
Which r-value suggests a strong negative correlation? A. r=0.97351 B. r= -0.27331 C. r= -0.97351 D. r= 0.27331
please help! im bad at this!
Assume that when adults with smartphones are randomly selected, 46% use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that at least 6 of them use their smartphones in meetings or classes.
Answer:
0.18173219.
Step-by-step explanation:
We have been asked to find what will be the probability that at least 6 of 9 adults use their smartphones in meetings or classes.
We will find our answer using Bernoulli's trails.
[tex]_{r}^{n}\textrm{c}\cdot p^{r}\cdot (1-p)^{n-r}[/tex]
First of all we will find the probabilities when r is 6, 7,8 and 9 then we will add them all.
When r=6,
[tex]_{6}^{9}\textrm{c}\cdot 0.46^{6}\cdot (1-0.46)^{9-6}[/tex]
[tex]\frac{9!}{6!3!} *0.46^{6} *0.54^{3}[/tex]
[tex]\frac{9*8*7*6!}{6!*3*2*1} *0.009474296896*0.157464[/tex]
[tex]84*0.009474296896*0.157464=0.12532[/tex]
Similarly we will find Probabilities when r=7, 8 and 9.
When r=7
[tex]_{7}^{9}\textrm{c}\cdot 0.46^{7}\cdot (1-0.46)^{9-7}[/tex]
[tex]\frac{9!}{7!2!} *0.46^{7} *0.54^{2}[/tex]
[tex]\frac{9*8*7!}{7!*2*1} *0.00435817657216*0.2916[/tex]
[tex]36*0.00435817657216*0.2916=0.04575039[/tex]
When r=8
[tex]_{8}^{9}\textrm{c}\cdot 0.46^{8}\cdot (1-0.46)^{9-8}[/tex]
[tex]\frac{9!}{8!1!} *0.46^{8} *0.54[/tex]
[tex]\frac{9*8!}{8!*1!} *0.00200476*0.54[/tex]
[tex]9 *0.00200476*0.54=0.0097431336[/tex]
When r=9,
[tex]_{9}^{9}\textrm{c}\cdot 0.46^{9}\cdot (1-0.46)^{9-9}[/tex]
[tex]\frac{9!}{9!0!} *0.46^{9} *1[/tex]
[tex]1 *0.00092219*1=0.00092219[/tex]
Now let us add all the probabilities to get the final answer.
[tex]0.12532+0.04575+0.00974+0.00092219=0.18173219[/tex]
Therefore, probability that at least 6 of 9 adults use their smartphones in meetings or classes is 0.18173219.
The probability that at least [tex]6[/tex] out of [tex]9[/tex] adult use their smartphone in meeting or classes is [tex]\fbox{\begin\\\ 0.1817\\\end{minispace}}[/tex].
Further explanation:
It is given that [tex]46\%[/tex] smartphone user use their smartphone in meetings or classes and at least [tex]6[/tex] out of [tex]9[/tex] adult smartphone user are selected randomly.
Here we will use the concept of Binomial probability.
If an experiment is performed [tex]n[/tex] times and it has only two outcomes that is, “success” and “failure”.So, the probability associated with this experiment is called Binomial probability.
The probability to get exactly [tex]r[/tex] successes in [tex]n[/tex] trial is given as follows,
[tex]\boxed{P=^{n}C_{r}p^{r}(1-p)^{n-r}}[/tex] ......(1)
Here, [tex]P[/tex] is the probability of [tex]r[/tex] successes in [tex]n[/tex] trials.
About [tex]46\%[/tex] smartphone user use their smartphone in meetings or classes that means the probability of the smartphone user use their smartphone in meetings or classes is as follows:
[tex]\begin{aligned}46\%&=\dfrac{46}{100}\\&=0.46\end{aligned}[/tex]
The statement, “at least six smartphone user” means six or more smartphone user. We will calculate the probability of the [tex]6,7,8[/tex] and [tex]9[/tex] adult smartphone user.
Substitute [tex]0.46[/tex] for [tex]p[/tex], [tex]9[/tex] for [tex]n[/tex] and [tex]6,7,8,9[/tex] for [tex]r[/tex] in equation (1) to obtain the probability of summation as follows,
[tex]P=^{9}C_{6}(0.46)^{6}(1-0.46)^{9-6}+^{9}C_{7}(0.46)^{7}(1-0.46)^{9-7}+^{9}C_{8}(0.46)^{8}(1-0.46)^{9-8}+\qquad^{9}C_{9}(0.46)^{9}(1-0.46)^{9-9}\\\\P=\dfrac{9!}{6!\cdot(9!-6!)}\cdot(0.46)^{6}\cdot(0.54)^{3}+\dfrac{9!}{7!\cdot(9!-7!)}\cdot(0.46)^{7}\cdot(0.54)^{2}+\dfrac{9!}{8!\cdot(9!-8!)}\cdot(0.46)^{8}\cdot(0.54)^{1}+\dfrac{9!}{9!\cdot(9!-9!)}\cdot(0.46)^{9}\cdot(0.54)^{0}[/tex]
Further solving the above equation as follows,
[tex]\begin{aligned}P&=84\cdot(0.46)^{6}\cdot(0.54)^{4}+36\cdot(0.46)^{7}\cdot(0.54)^{2}+9\cdot(0.46)^{8}\cdot(0.54)^{1}+1\cdot(0.46)^{9}\cdot(0.54)^{0}\\&=0.1253+0.04575+0.009743+0.00092219\\&=0.1817\end{aligned}[/tex]
Therefore, the probability that at least [tex]6[/tex] out of [tex]9[/tex] adult use their smartphone in meeting or classes is [tex]\boxed{0.1817}[/tex].
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Answer details:
Grade: College
Subject: Mathematics
Chapter: Probability
Keywords: Probability, numbers, chances, smartphone, meeting, classes, 0.1817, summation, user, equation, selected, Binomial probability, randomly.
MATH HELP PLEASE WILL GIVE BRAINLIEST!!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
The price of a math book is $50, but you have only $35 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?
Stretch Your Thinking Ann arranges her marbles in groups, with 8 marbles in each group. She writes the fraction 5/8 to show the fraction of marbles in each group that is red. What equivalent fraction names the fraction of marbles in 6 groups that are Red? Explain.
What is the measure of angle x?
Enter your answer in the box.
x = °
Answer:
I also got 43 using the same strategy as the first guy.
Step-by-step explanation:
90*-40*=43*
please help me, thanks.