Answer: 56.50
Step-by-step explanation:
75 divided by 2 = 37.50
37.50 divided by 2 = 18.75
75 - 18.75 = 56.25
Hope this helps!
Find the area of each triangle to the nearest tenth.
The area of triangle RST is approximately 94.77 square centimeters.
We have,
To find the area of a triangle RST, we can use the formula for the area of a triangle:
Area = (1/2) x base x height
In this case, we have the lengths of two sides of the triangle (TR = 14 cm and SR = 9 cm) and the measure of an angle (∠SRT = 81 degrees). However, we do not have the height of the triangle directly.
To find the height, we can use trigonometry.
We know that the sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In triangle RST, the side opposite angle ∠SRT is SR, and the hypotenuse is TR.
sin(∠SRT) = SR / TR
sin(81) = 9 / 14
Now, we can solve for the height (h) using the sine ratio:
h = TR x sin (∠SRT)
h = 14 x sin (81)
Using a calculator, we find h ≈ 13.71 cm (rounded to two decimal places).
Now, we can calculate the area of triangle RST:
Area = (1/2) x base x height
Area = (1/2) x TR x h
Area = (1/2) x 14 cm x 13.71 cm
Area = 94.77 cm² (rounded to two decimal places)
Therefore,
The area of triangle RST is approximately 94.77 square centimeters.
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Wendy makes tacos. The model shows the ratio relationship for the ingredients.
What is the ratio of cups of chicken to taco shells? Choose all the
correct answers.
Taco shells
9
Cups of chicken
4
According to the information, the ratio of taco shells and cups of chicken is 9:4.
How to identify the ratio of Taco shells and cups of Chicken?To identify the ratio of Taco shells and cups of chicken we must take into account the information in the image. In this case we must count how many units of each element we have. So we have 9 Taco shells and 4 cups of chicken.
According to the above, the ratio would be 9:4, that is to say that for every 9 taco shells that we have, we would have to use 4 cups of chicken. Therefore, if we want to double or triple the recipe we must use the following ingredients:
Double
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A small radio can broadcast in a circular range with a radius of 12 miles. How many square miles is the area covered by this range.
The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax = 0?
a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.
(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.
(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:
nullity = number of columns - rank
nullity = 3 - 2 = 1
Therefore, the nullity of matrix A is 1.
(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
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3 tacos cost $18. complete the table to show the cost of 4,5 and 6 tacos at the same rate
x y
4 24
5 30
6 36
cost per taco: $6 dollars
*The x and y is the x and y coordinates for the table
one day, a downtown hotel in san jose had to walk a guest to another hotel. the room rate for another hotel in downtown was $150. it cost $15 for the guest to take an uber to another hotel. the overbooked hotel also gave the guest a gift card of $25. how much is the cost of walking this guest? group of answer choices $150 $180 $190 $160
The cost of walking this guest is $190.
The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.
The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.
In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.
Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.
Therefore, the total cost incurred by the hotel for walking the guest is:
$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190
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What is the equation of the line that passes through the point (-3, -8) and has a
slope of 4?
y = 4x + 4
Step-by-step explanation:The equation of a line is most commonly given in the slope-intercept form.
Slope-Intercept Form
Slope-intercept form is given by the formula y=mx+b, where m is the slope and b is the y-intercept. This form is most commonly used because it is easy to draw a graph from and it is very concise. We already know one of the constants, m = 4. So, to find the equation we need to solve for b.
Solving For b
To solve for b, we need to plug in all of the information that we are given into the formula. We are given 3 pieces of info for this point: y = -8, x = -3, m = 4.
-8 = -3(4) + bThen, multiply.
-8 = -12 + bFinally, add 12 to both sides.
4 = bNow that we know the value of b, we can go back to the formula and plug in both constants, y = 4x + 4.
find the values ox x and y that make the quadrilateral a parallelogram, please show how you did it
At the Petite École Internationale Day Care, the diapers are changed every 2 hours. The day care workers believe 15% of the diapers leak before they are changed. When the diapers are changed, about 70% are full. The workers have noticed that of the diapers that are full, around 20% leak. Given that a diaper has leaked, what is the probability that the diaper is full?
Answer:
The probability that the diaper is full given that it has leaked is 0.105
Step-by-step explanation:
The given parameters are;
The percentage of diapers that leak before they are changed = 15%
The percentage of diapers that are full when they get changed = 70%
The percentage of full diapers that that leak = 20%
Therefore, given that the percentage of the changed diapers that are full = 70% and out of the full diapers that leak = 20%
∴ The probability that the diaper is full given that it has leaked = The percentage of diapers that leak before they are changed × The percentage of diapers that are full when they get changed
The probability that the diaper is full given that it has leaked = 15/100 × 70/100 = 21/200 = 0.105
The probability that the diaper is full given that it has leaked = 0.105
Answer: The probability that the diaper is full given that it has leaked is 0.105.
What is the ordered pair for Point T?
A. (1,5)
B. (0,5)
C. (5,0)
D. (5, 5
Answer:
B.(0,5)
Step-by-step explanation:
Ordered pairs are written as (x,y)
x value of T is 0
y value of T is 5
Ordered pair for point T is (0,5)
Suppose the solution set of a certain system of linear equations can be described as x_1 = 6 + 3x_3, x_2 = -2 - 5x_3, with x_3 free. Use vectors to describe this set as a line in R^3. Geometrically, the solution set is a line through parallel to
The solution set of the given system of linear equations can be expressed as a line in R^3 vector as r = (6, -2) + x_3(3, -5).
To express the solution set of the given system of linear equations as a line in R^3, we first need to express the solution set as a vector equation. We can do this by expressing the equations in terms of x_3 as follows:
x_1 = 6 + 3x_3,
x_2 = -2 - 5x_3
Therefore, the solution set of the given system of linear equations can be expressed as a line in R^3 as follows:
r = (6, -2) + x_3(3, -5).
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automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. the following table is a frequency distribution of speeds. speed (miles per hour) frequency 45 up to 55 50 55 up to 65 325 65 up to 75 275 75 up to 85 25 how many of the cars traveled less than 75 miles per hour?
To find out how many of the cars traveled less than 75 miles per hour, we need to add up the frequency of the first three categories: 45 up to 55, 55 up to 65, and 65 up to 75.
50 + 325 + 275 = 650
So, 650 cars traveled at a speed less than 75 miles per hour.
Based on the provided frequency distribution, we can determine the number of cars traveling less than 75 miles per hour by adding the frequencies of the relevant speed ranges:
- 45 up to 55: 50 cars
- 55 up to 65: 325 cars
- 65 up to 75: 275 cars
To calculate the total number of cars traveling less than 75 miles per hour, add the frequencies:
50 cars (45-55 mph) + 325 cars (55-65 mph) + 275 cars (65-75 mph) = 650 cars
So, 650 cars traveled less than 75 miles per hour.
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PARALLEL PERPENDICULAR OR NEITHER OR SAME LINE
Answer:
Perpendicular
Step-by-step explanation:
Let's start by finding the slopes of both lines.
Line A's slope is 3 (this is given).
We can determine line B's slope with the two points given. The slope formula is \(m=\frac{y1-y2}{x1-x2}\). Substitute in the values:
\(m=\frac{1-(-1)}{-3-3}\)
and simplify:
\(m=\frac{2}{-6}\)
So the slope of line A is -1/3.
-1/3 and 3 multiply to -1, so this indicates that the two lines are perpendicular.
Answer:
Perpendicular
Step-by-step explanation:
If Line A passes through the origin with a slop of 3, then Line A would be
y = 3x
For Line B, using the slope/points method, the line would be
y = -1/3x
When graphing these two lines, they intersect as opposite slopes, so therefore this pair of equations would be Perpendicular
A veterinarian records the weights of several puppies over an 8-week period, beginning when each puppy is 12 weeks of age. This equation describes the relationship between the number of weeks, x, after a puppy’s weight is first recorded and the puppy’s weight, y, in pounds. y = 2.5x + 26.5 The number 26.5 in the equation represents the average number of pounds that a puppy weighs at 12 weeks of age. a puppy weighs at 20 weeks of age. a puppy’s weight increases over the 8-week period. a puppy’s weight increases during each of the 8 weeks.
Answer: The number 26.5 in the equation represents the average number of pounds that a puppy weighs at 12 weeks of age.
To find the weight of a puppy at 20 weeks of age, we can substitute x = 20 into the equation:
y = 2.5x + 26.5
y = 2.5(20) + 26.5
y = 50 + 26.5
y = 76.5
Therefore, a puppy weighs approximately 76.5 pounds at 20 weeks of age.
The equation y = 2.5x + 26.5 represents a linear relationship between the number of weeks after a puppy's weight is first recorded and the puppy's weight in pounds. Since the coefficient of x is positive, this means that a puppy's weight increases over time. Specifically, the weight increases by 2.5 pounds for each additional week.
However, the equation does not tell us whether a puppy's weight increases during each of the 8 weeks. To determine this, we would need additional information such as the weights of the puppies at different points in time over the 8-week period.
Step-by-step explanation:
The ratio of the amount o rice Max has to the amount of rice Victor has to the amount of rice Roman has is 3:2:4, If Victor gives 1/4 of hs rice to Roman, what will the new ratio of the amounts of Max's rice to Victor's rice be
The new ratio of the amounts of Max's rice to Victor's rice to Roman's rice is 2:1:3.
Given, that ratio of rice between max, victor and roman
Ratio : A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let the amount of rice that Max, Victor, and Roman have as 3x, 2x, and 4x, respectively.
The total ratio of the amounts of rice is 3+2+4 = 9,
So each "part" of the ratio is 1/9.
If Victor gives 1/4 of his rice to Roman, he will give away
(1/4) × (2x) = 1/2x rice to Roman, and he will be left with
(3/4) × (2x)
= 6/4x
= 3/2x rice.
Roman will receive 1/2x rice from Victor and will have
4x + 1/2x = 9/2x rice in total.
So the new amounts of rice that Max, Victor, and Roman have are 3x, 3/2x, and 9/2x, respectively.
The new ratio of the amounts of rice is (3x):(3/2x):(9/2x).
To simplify this ratio, we can multiply all parts by 2 to get:
6x:3x:9x
And then divide all parts by 3x to get:
2:1:3
Hence, the new ratio of the amounts of Max's rice to Victor's rice to Roman's rice is 2:1:3.
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The new ratio of the amount of rice that Max has to the amount that Victor has after Victor gives away 1/4 of his rice to Roman is 2:1.
Explanation:Let's assume the amount of rice Max, Victor, and Roman have are 3x, 2x, and 4x units respectively. Now, if Victor gives 1/4 of his rice to Roman, Victor's amount will decrease by 1/4*2x = 0.5x, therefore, Viktor will have 2x - 0.5x = 1.5x units of rice. So, the new ratio of the amount of rice Max to the amount of rice Victor will be 3x:1.5x or, simplifying, 2:1.
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3. Sleeping Beauty loves to sleep. Every weekday, she makes sure that
she gets the complete 8-hour sleep. However, every weekend, she only
sleeps for 6 hours because she likes to party. What is her total sleeping
hours for a month, given that a month has only 4 weeks?
Answer:
208
Step-by-step explanation:
There are 5 weekdays in a week and 2 weekend days. Since there are 4 weeks, multiply 5 times 4 to get 20 weekdays/month, and 2 times 4 to get 8 weekend days/month. 20 times 8 (the hours she sleeps) is 160 hours, and 8 times 6 is 48 hours. Put together, you get 208 total hours.
23, 69, 207 7th term
Answer:
16767
Step-by-step explanation:
Each new term is found by multiplying the previous term by 3. Thus, 3 is the common ratio. The formula for this geometric series is therefore
a(n) = 23*3^(n - 1).
The 7th term is a(7) = 23*3^6 = 16767
suppose f : rn → rm is a linear map. what is the derivative of f ?
If f: rn → rm is a linear map, then its derivative is simply the map itself. This is because a linear map is a function that preserves vector addition and scalar multiplication.
In other words, if we take two vectors in the domain and add them together, and then apply the linear map, it is the same as applying the linear map to each vector separately and then adding the results. Similarly, if we multiply a vector in the domain by a scalar and then apply the linear map, it is the same as multiplying the result of applying the linear map to the original vector by the same scalar.
Formally, we can express this idea using the concept of a Jacobian matrix. The Jacobian matrix of a function describes the rate at which the function changes near a particular point. For a linear map, the Jacobian matrix is simply the matrix that represents the map. This means that the derivative of f is the matrix A such that f(x) = Ax for all x in rn.
To see why this makes sense, consider the simplest case of a linear map from R1 to R1, given by f(x) = ax, where a is a constant. The derivative of this function is f'(x) = a, which is just the constant coefficient of the linear map. More generally, the derivative of a linear map f: rn → rm is the matrix A such that f(x) = Ax for all x in rn.
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g(x)=8x^3+1 Find the difference quotient
The different quotient for f(x)=8x³+1 is 8(-x³+(h+x)³)/h.
What is a quotient?In mathematics, a quantity created by the division of two numbers is known as a quotient (from the Latin quotiens, meaning "how many times"; pronunciation: /kwont/). The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (in the case of Euclidean division), as well as a fraction or a ratio (in the case of proper division). As an illustration, the quotient of the division of 20 (the dividend) by 3 (the divisor) is in the Euclidean sense of remaining and 6 2/3 in the appropriate division sense. In the second definition, a quotient consists just of the dividend to divisor ratio.it is given that, g(x)=8x³+1
The difference quotient is given by f(x+h)-f(x)/h
to find f(x+h), put x+h instead of x:
then, f(x+h)=8(x+h)³+1
finally, = f(x+h)-f(x)/h
=(8(x+h)³+1))-(8x³+1)/h
=8(-x³+(h+x)³)/h
Hence, The different quotient for f(x)=8x³+1 is 8(-x³+(h+x)³)/h.
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What is the joint relative frequency for 11th graders who want the break in the afternoon? Round to the nearest percent.
Answer:
21%
Step-by-step explanation:
just got it right on edg
Which of these numbers had exactly tow factors?
Select your answer. 7 8 9 10
A B C D
Answer:
prime numbers only have two factors...
7 is the only prime in the list
Step-by-step explanation:
PLSSSSS HELP!!
The graph below shows the price of different numbers of mats at a store: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 21, 42, 63, 84, and 105. Points are shown on ordered pairs 0, 0 and 2, 21 and 4, 42 and 6, 63 and 8, 84. These points are connected by a line. The label on the x axis is Number of Mats. The title on the y axis is Price in dollars. Which equation can be used to determine p, the cost of b mats? p = 10.50 + b b = 10.50 + p b = 10.50p p = 10.50b
Answer:
p = 10.50 + b b = 10.50 + p b = 10.50p p = 10.50b
Step-by-step explanation:
The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 21, 42, 63, 84, and 105. Points are shown on ordered pairs 0, 0 and ..
The graph below shows the price of different numbers of mats at a store: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 21, 42, 63, 84, and 105. Po - the ... 21, 42, 63, 84, and 105. Points are shown on ordered pairs 0, 0 and 2, 21 and 4, 42 and 6, 63 and 8, 84.
Answer:
p = 10.50 + b b = 10.50 + p b = 10.50p p = 10.50b
Step-by-step explanation:
a student takes a true-false test that has 14 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(5) group of answer choices 0.0001 0.0611 0.1833 0.1222
The probability to answer 5 questions correctly from 14 true or false questions is 0.1222
The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:
P(x)= nCx × p^x × q^(n-x)
Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.
n = 14 (total number of questions)
p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).
To find P(5), we substitute these values in the formula
P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222
Therefore, the answer is option D, 0.1222.
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Suppose a die is loaded die. it is biased so that an outcome of 4 is three times as likely to occur as the other numbers. what is the probability that a four shows up when this die is rolled?
The probability of rolling a four with the loaded die is 1/3.
To find the probability of rolling a four with a loaded die, we need to determine the likelihood of that specific outcome occurring.
In this case, we are told that a four is three times as likely to occur as the other numbers. This means that the probability of rolling a four is three times greater than the probability of rolling any other number on the die.
Let's assume that the probability of rolling any other number on the die is represented by "x". Since the probability of rolling a four is three times greater, we can represent it as "3x".
To find the value of "x", we need to consider the total probability of all possible outcomes. In this case, we have six possible outcomes (numbers 1 to 6), and the probability of each outcome must sum up to 1 (or 100%).
Therefore, we can set up the following equation: x + x + x + x + x + 3x = 1.
Simplifying the equation, we have: 6x + 3x = 1.
Combining like terms, we get: 9x = 1.
Dividing both sides by 9, we find: x = 1/9.
So, the probability of rolling any other number on the die (besides a four) is 1/9.
Now, to find the probability of rolling a four, we substitute the value of "x" back into our equation. Since 4 is three times more likely, the probability of rolling a four is:
3 * (1/9) = 3/9
= 1/3.
Therefore, the probability that a four shows up when this loaded die is rolled is 1/3.
Conclusion: The probability of rolling a four with the loaded die is 1/3.
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Meredith deposits $1,400 into an account that earns 3% annual simple interest. How many years will it take Meredth to earn $294 in simple interest on the account?
Answer:
21 years
Step-by-step explanation:
Joe goes to the store to buy milk that cost x + $3, bread that cost x + $2.25, and 3 bags of potato chips that cost x + $1.50 each. Write an equivalent expression to represent what he spent.
Given:
Milk cost = x + $3,
Bread cost = x + $2.25,
3 bags of potato chips cost = x + $1.50 each.
To find:
The equivalent expression to represent what he spent.
Solution:
1 bag of potato chips cost = x + $1.50
3 bag of potato chips cost = 3(x + $1.50).
Total cost = Milk cost + Bread cost + Cost of 3 bags of potato chips
\(\text{Total cost}=(x+\$3)+(x+\$2.25)+3(x+\$1.50)\)
\(\text{Total cost}=x+\$3+x+\$2.25+3x+\$4.50\)
\(\text{Total cost}=(x+x+3x)+\$(3+2.25+4.50)\)
\(\text{Total cost}=5x+\$9.75\)
Therefore, the required expression is 5x+$9.75.
ple help me whats the slope?
Answer:
-4/3
Step-by-step explanation:
that is the answer...no explanation needed
-4/3
y intercept- (0, -7)
2. find the general solution of the system of differential equations d dt x = 9 3 −3 9 x
The general solution of the system of differential equations is x = c1e^6t + c2e^2t, where c1 and c2 are constants.
To find the general solution, we first need to find the eigenvalues and eigenvectors of the matrix A = [9 -3; -3 9]. The characteristic equation is det(A - λI) = 0, where I is the 2x2 identity matrix. Solving for λ, we get λ1 = 6 and λ2 = 12.
For λ1 = 6, we have (A - λ1I)v1 = 0, where v1 is the corresponding eigenvector. Solving for v1, we get [1; 1]. Similarly, for λ2 = 12, we have (A - λ2I)v2 = 0, where v2 is the corresponding eigenvector. Solving for v2, we get [-1; 1].
The general solution can now be expressed as x = c1e^(λ1t)v1 + c2e^(λ2t)v2. Substituting the values of λ1, λ2, v1, and v2, we get x = c1e^(6t)[1; 1] + c2e^(12t)[-1; 1]. Simplifying this expression, we get x = c1e^(6t) + c2e^(12t), x = c1e^(6t) - c2e^(12t) for the two components respectively.
These are the general solutions for the two differential equations.
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Two small buckets and 1 large bucket can hold 8 cups of gasoline. One large bucket minus 1 small bucket constitutes 2 cups of gasoline. How many cups of gasoline can each bucket hold?
Let's represent the capacity of the small bucket as "x" and the capacity of the large bucket as "y".
From the first statement, we can set up the equation:
2x + y = 8
From the second statement, we can set up another equation:
y - x = 2
Now we can solve for "x" and "y".
Rearranging the second equation, we get:
y = x + 2
Substituting this value of "y" into the first equation, we get:
2x + (x + 2) = 8
Simplifying, we get:
3x + 2 = 8
Subtracting 2 from both sides, we get:
3x = 6
Dividing by 3, we get:
x = 2
Substituting this value of "x" into the second equation, we get:
y - 2 = 2
Simplifying, we get:
y = 4
Therefore, each small bucket can hold 2 cups of gasoline, and the large bucket can hold 4 cups of gasoline.
Pls help Ill give brainiest or whatever
Answer:
2.5 hours
Step-by-step explanation:
it takes him 2.5 hours
Answer:
The time is 2.5 hours.
Step-by-step explanation:
7.5/3=2.5
hope this helps!