The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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last month maria hiked a total of 90 miles on two trails a 5 mile mountain trail and a 10 mile canal trail let x represent the number of times maria hiked the mountain trail and let y represent the number of times maria hiked the canal trail. which equation can be used to find the number of times maria hiked each trail
Answer:
5x + 10y = 90
Step-by-step explanation:
x represents the mountain trail which she walked 5 miles
y represents the canal trail which she walked 10 miles
A bag contains 2 gold marbles, 7 silver marbles, and 29 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss of you play this game?
Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
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5. A sphere with a diameter of
14 centimeters is filled with sand.
Roberto poured of the sand out of the
sphere. About how much sand is left in
the sphere?
A.
287.2 cm
B.
861.6 cm
C.
1,148.8 cm
D. 9,190.6 cm
The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.
What is the volume of the sphere?Let r be the radius of the sphere. Then the volume of the sphere will be given as,
V = 4/3 πr³ cubic units
Sand is contained within a spherical with a 14 centimeters diameter. Roberto emptied the sphere's contents of sand.
The radius of the sphere is given as,
r = d/2
r = 14 / 2
r = 7 cm
Then the volume of the sphere is given as,
V = (4/3) x π x (7)³
V = 1.33 x 3.14 x 343
V = 1,436.03
The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.
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The correct options are given below.
A. 287.2 cm³
B. 861.6 cm³
C. 1,148.8 cm³
D. 9,190.6 cm³
E. 1,436.03 cm³
Si en dos horas y media un motociclista ha cubierto una distancia de 320 kilómetros. ¿Ha superado el límite de velocidad previsto, que es de 80 km/h?
La velocidad promedio del motociclista es 128km/h, entonces si, supera el limite de velocidad previsto.
¿Ha superado el límite de velocidad previsto, que es de 80 km/h?Sabemos que podemos definir la velocidad como el cociente entre distancia y tiempo, en este caso sabemos que:
distancia = 320km
tiempo = 2.5 h.
Entonces la velocidad será:
v = 320km/2.5 h = 128 km/h
Podemos ver que claramente, el motociclista supera el limite de velocidad previsto.
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Consider the line 8x-5y=1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line ?
What is the solution to the system of equations?
{y=5x−10
{y=−3x+14
Enter your answer as the correct ordered pair, like this: (42, 53)
multiply the second equation by -1, you get
y=5x-10
-y=3x-14
add both of the equations together
0=8x-24
then
24=8x
x=3
to find y replace x in one of the original equations
y=5x-10
y=5(3)-10
y=15-10
y=5
(x,y)
(3,5)
division resultado
de residuo sea 400
A division problem that would lead to a division remainder of 400 is 2, 400 ÷ 500.
How to find the division problem ?You need to find a division problem where the quotient would be such that there would be a remainder of 400.
In that case, the first thing to do is to ensure that the divisor is greater than 400. If it is less, then the remainder cannot be 400.
We can the pick the next hundred after 400 which would be 500. Then, we need to find a number that when divided by 500, would result in 400 as a remainder.
This can be 900, 1, 400, 1, 900, 2, 400 etcetera.
The trick is to ensure that the number is 400 more than a multiple of 500.
Picking 2, 400, the division is therefore:
= 2, 400 ÷ 500
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A large bamboo plant is 3 times as tall as a small bamboo plant. If the large plant is 16.5 feet tall, how tall is the small bamboo plant?
Answer:
The small bamboo plant is 5.5 feet tall
Step-by-step explanation:
I (1) = 16.5 ft, 3 times as tall as II
II (2) = ? ft
Let the first be x and the second be y, Than
x = 16.5 ft
x = 3y
y = x / 3
y = 16.5 / 3
y = 5.5 ft
An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
a. 4
b. 16
c. 8
d. 32
16 sample points (possible outcomes as to the classifications) exist.
What is the combination?
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
Here, we have
Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.
There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.
A total of (4)(4) = 16 sample points.
Hence, 16 sample points (possible outcomes as to the classifications) exist.
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A passenger train traveled 240 miles in the same amount of time it took a freight train to travel 160 miles. The rate of the freight train was 20 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
The rate of the passenger's train is given as follows:
60 miles per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
For the passenger train, the equation is given as follows:
v = 240/t.
vt = 240
t = 240/v.
For the freight train, the velocity is 20 miles slower than for the passenger train, hence:
v - 20 = 160/t
v = 160/t + 20.
Replacing the first equation into the second, the rate of the passenger train is obtained as follows:
v = 160v/240 + 20
v = 2v/3 + 20
v/3 = 20
v = 60 miles per hour.
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A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and
twice the reciprocal of the larger is 9/10 then find the two integer
Answer:
Step-by-step explanation:
Let the smaller integer be x, then the larger integer is x + 3.
The sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/10:
1/x + 2/(x + 3) = 9/10
Expanding both sides:
10/x + 20/(x + 3) = 90/10
Combining like terms on the left side:
(10 + 20)/(x(x + 3)) = 90/10
30/(x(x + 3)) = 9/10
Cross multiplying both sides:
30 * 10 = 9 * (x(x + 3))
300 = 9x(x + 3)
Expanding the right side:
300 = 9x^2 + 27x
Subtracting 27x from both sides:
273 = 9x^2 + 27x - 27x
273 = 9x^2
Taking the square root of both sides:
√273 = √(9x^2)
√273 = 3x
Dividing both sides by 3:
√273/3 = x
The smaller integer is √273/3 and the larger integer is √273/3 + 3.
Given the following parallelogram, solve for x.
X =
(18x - 79) °
(7x + 9) °
how many groups of 1/2 in a 8
Answer:
Step-by-step explanation:
y=16. There are sixteen 1/2 in 8
PREMISES
y=8/.5
CALCULATIONS
y=8/.5
y=8(2)
y=
16
PROOF
If y=16, then the dependent value D(y) 8/.5 returns
y(.5)=8
Suppose we have a bag of jelly beans 82% of the jelly beans orange, 14% are black, and 4% are green. Moreover, 15% of orange are sugar free, 70% of black beans are sugar free, and 90% of green beans are sugar free Suppose we select a jelly bean at random.
1. Construct a tree diagram to represent this situation
2. Find the probability of green bean and sugar free
3. Given the bean is sugar free, what is the probability that it is an orange bean?
Please I need help
Answer:
3/50
Step-by-step explanation:
3 g, 5 r, 2 o
3 + 5 + 2 = 10
Orange = 2 jelly beans
Probability of selecting an orange jelly bean: 2/10 or 1/5
If you put the jelly bean back in, there is still 10 jelly beans.
Green = 3 jelly beans
Probability of selecting a green jelly bean: 3/10\
Multiply the probabilities:
1/5 x 3/10
= 3/50
What equation would you use to solve x
Answer: X^2+6.8^2=10.6^2
Step-by-step explanation:
The pythagorean theorem can be used to find the missing sides of triangles.
The formula is:
a^2+b^2=c^2, where c^2 is always the hypotenuse (the biggest and diagonal line) and a^2 and b^2 are the other side lengths
In this problem, plug in the values. So in this case, you have:
a^2+6.8^2=10.6^2
Hope this helps
the equation of a curve is given by
y=x^3/3+7x^2/2+10x+d, where d is a
constant. Find the possible values of d
when the x-axis is tangent to the curve
v=x^3/3+7x^2/2+10x+d.
Answer: The x-axis is tangent to the curve when the value of y is equal to 0. So, to find the possible values of d when the x-axis is tangent to the curve, we need to solve the equation:
x^3/3 + 7x^2/2 + 10x + d = 0
To solve this equation, we need to use a method such as the cubic formula or a numerical method such as Newton-Raphson. However, it is not possible to determine a general solution for d without additional information, such as the value of x at which the tangency occurs. The possible values of d will depend on the specific value of x that satisfies the equation.
Step-by-step explanation:
Circles and answers please just need help please sap
On solving the provided question, we can say that x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
x = central angle = 60 degrees
r = radius = 9 inches
L = arc length
[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]
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K
In 1999 there were 60 million people worldwide who had been infected with a particular disease. At that time the infection rate was 3.5 million people per year.
(a) Write a formula for a linear function that models the total number of people in millions who were infected with the particular disease x years after 1999.
(b) Estimate the number of people who may have been infected by the year 2013.
f(x) = ax + b, where a and b are real values, is the formula for a linear function. In this instance, a denotes the line's gradient, and b denotes the y-axis intercept (which is sometimes called the vertical intercept).
What is linear function?A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y. Look for a steady rate of change to determine whether a table of values depicts a linear function. You are viewing a linear function if there is one!To learn more about linear function, refer to:
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Find the value of X
Please help! Asap
Answer:
Step-by-step explanation:
More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and now, a cure could be in sight. Source: The Guardian, November 30, 2018 Make a graph of the production possibilities frontier with HIV/AIDS cases treated on the x-axis and other goods and services on the y-axis before and after the advance in technology. Question content area bottom left Part 1 The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated. Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0. Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
The production possibility frontier based on the information is attached.
What is the PPF about?PPF0 is the curve before technological progress. PPF1 is the the curve after the advance in technology.
Before the advance in technology, the opportunity cost of treating HIV/AIDS increases as the world moves down along its PPF.
After the advance in technology, the opportunity cost of treating more HIV/ AIDS cases decreases as the world has to give up less other goods and services to treat additional HIV/AIDS patients. Or, by giving up the same amount of other goods and services, world can treat more HIV/AIDS patients now.
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Margo borrows $600, agreeing to pay it back with 2% annual interest after 10 months. How much interest will she pay? Round your answer to the nearest cent, if necessary
The amount of interest paid will be $9.6.
What is simple interest?The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.
Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.
The simple interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 600 x 2 x 0.8 ) / 100
SI = 960 / 100
SI = $9.6
Therefore, $9.6 will be paid in interest.
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If f(x) = x sinx/1+cos x find f'(π/2).
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
f'(π/2) = π/2 + 1.Kindly refer the attachment.Step-by-step explanation:
Hope it helps you~**Image **Find the value of x. Show your steps.
The value of x is 9 by using the concept of corresponding angles.
What are corresponding angles?Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.
From the information given:
(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.
Using the sum of angles on a straight line.
Step 1: (8x + 9)° + 99 = 180°
Step 2: 8x + 108 = 180
Step 3: 8x = 72
Step 4: x = 9
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well asap due today pls
Answer:
96 in²
Step-by-step explanation:
Length of Semiperimeter
[tex]\displaystyle s=\frac{1}{2}(a+b+c)=\frac{1}{2}(12+16+20)=\frac{1}{2}(48)=24[/tex]
Area of Triangle w/Heron's Formula
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-12)(24-16)(24-20)}=\sqrt{24(12)(8)(4)}=\sqrt{9216}=96[/tex]
Hence, the area of the triangle is 96 in².
When put on a coordinate plane, 1st street has the equation y = 6x - 7. 2nd street is parallel to 1st street and
goes through the point (2, 9). Write the equation for 2nd Street in slope-intercept form.
by
The linear equation for the parallel line will be y=6x-3.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
Line parallel to line y=6x-7 will have same slope which will be m=6
as general equation is y=mx+c where m=slope and c=constant.
For parallel line c will be as it is passing through (2,9)
9=6*2+c
c=9-12
c=-3
then the equation will be y=6x-3
Hence,
The equation for the parallel line will be y=6x-3.
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Whats the correct answer answer asap for brainlist
The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.
Definition of the word "obstinancy", its uses and example:Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.
We often use the word "obstinancy" for the followings:
to describe someone's persistence in pursuing a particular course of action despite obstacles or challenges.to describe someone's reluctance to change their opinion or attitude in light of new evidence.to describe someone's refusal to give in to the demands or requests of others.Read more about Obstinancy
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A mechanic had412 gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answer:
3,291 pints used
Step-by-step explanation:
There are 8 pints in a gallon
Started with 412 gallons, multiply that by 8 to get 3,296 pints
At the end of day, he only had 5
So we can subtract 5 from the 3,296 that he started the day with, and we get the answer of 3,291 used throughout the day.
Solve for x and simplify answer
4
\x=-18
3
The value of the variable is x = -6/9
What is a fraction?A fraction is defined as the part of a whole number.
The different types of fractions are;
Mixed fractionsSimple fractionsComplex fractionsImproper fractionsProper fractionsWe are given the equation:
4/x = -18/3
To make 'x' the subject, cross multiply
-18x = 12
Now, divide both sides by the coefficient of x, we get;
x = 12/-18
x = -6/9
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(6 points) Here are the data on the age for a random sample of instructors working in three different colleges. Use appropriate
99%
confidence intervals to complete the each of the following questions . Part A We are
99%
confident that the mean age of all instructors in College
A
is College B by between years old and (Round the numeric answers to 5 decimal places) Part B We are
99%
confident that the mean age of all instructors in College
A
is College C by between (Round the numeric answers to 5 decimal places) Part E We are
99%
confident that the mean age of all instructors in College B is College C by between years old and years old. (Round the numeric answers to 5 decimal places)
Part A: We are 99% confident that the mean age of all instructors in College A is between 42.79128 and 51.2088 years old.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 37.36368 and 54.63632 years old.
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
In this question, they are asking to calculate the 99% confidence intervals for the mean age of instructors in three different colleges (A, B, and C). They want to compare the mean age of instructors in College A to College B, College A to College C, and College B to College C. The numeric answers should be rounded to 5 decimal places.
To calculate these confidence intervals, you need to find the sample mean and standard deviation of the data for each college. Then, you can use the formula for a two-sample t-test to calculate the confidence intervals. The formula is (sample mean A - sample mean B) ± t-critical value * (standard deviation of A/√nA + standard deviation of B/√nB), where nA and nB are the sample sizes for Colleges A and B, respectively.
Part A: We are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation of the sample data. The mean age of all instructors in College A is 22.273 and the standard deviation is 1.936.
Next, we must use the t-distribution to calculate the 99% confidence interval. The critical value is 2.228. The confidence interval is calculated as follows:
Lower Bound = 22.273 - (2.228 x 1.936) = 20.81733
Upper Bound = 22.273 + (2.228 x 1.936) = 23.72867
Therefore, we are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 17.73173 and 25.71367.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
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3. Explain how "a" affects the graph of a parabola. (f(x) = ax²)
The effect of "a" in the graph of parabola is value from the quadratic function.
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
y = a(x – h)2 + k or x = a(y – k)2 +h
Where:
(h, k) - The vertex of the parabola.
p - Least distance between the vertex and the focus of the parabola.
Given that;
The equation of parabola is f(x) = ax².
Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.
We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.
Therefore, the role of a in parabola is stated.
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