subtract 28 from both sides ....
2x+28-28=40-28
2x= 12
x=12 Ans........
thank you!
Solve for x questions in picture
Answer:
x = 62
Step-by-step explanation:
2x ÷ 2 = 124 ÷ 2
x = 124 ÷ 2 = 62
Given sin(-t) = 2/3, find csc (t).
Answer:
csc(t) = -3/2
Step-by-step explanation:
Given sin(-t) = 2/3, we can find the value of csc(t) as follows:
sin(-t) = 2/3
sin(t) = -2/3 (since the sine function is an odd function)
Since csc(t) = 1/sin(t), we have:
csc(t) = 1/sin(t) = 1/(-2/3) = -3/2
Answer:
[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]
The second step can be done because sin(-t) is an odd function.
What are the zeros and a -intercepts for the function below?
f(x) = 2x² + 14x + 20
Step-by-step explanation:
the zeros are the x-intercepts. because these are x values, when y (= f(x)) = 0.
a quadratic equation has 2 zeros (even if they are equal or complex numbers).
a quadratic equation
ax² + bx + c = 0
can always be solved by
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-14 ± sqrt(14² - 4×2×20))/(2×2) =
= (-14 ± sqrt(196 - 160))/4 =
= (-14 ± sqrt(36))/4 = (-14 ± 6)/4
x1 = (-14 + 6)/4 = -8/4 = -2
x2 = (-14 - 6)/4 = -20/4 = -5
these are the 2 zeros (x-intercepts).
if you need the explicit points :
(-5, 0) and (-2, 0)
the y-intercept is the y-value when x = 0
y = 2×0² + 14×0 + 20 = 20
the explicit point : (0, 20)
Mathematics: What is a mean
Solve for x.
-x+8=259
X =
Answer:x=251
Step-by-step explanation:
Step 1: Subtract 8 from both sides of the equation.
Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.
Step 2: x = 251
Explanation: Subtracting 8 from both sides of the equation gives us
x = 259 - 8 = 251.
Answer:
Step-by-step explanation:
x = -251
Paul came in with a discovery about subtracting integers. Rather than subtracting, Paul says all he has to do I add the opposite of the second number, Create a subtraction problem with integer tiles and check out Paul's claim. Is paul right?
Answer:
Subtracting integers can be represented using integer tiles. For example, if we want to subtract -3 from 4, we can lay out 4 tiles on the number line and then add -3 tiles, like this:
4 3 2 1 0 -1 -2 -3
The subtraction problem can be represented as 4 + (-3). Adding the opposite of the second number, as Paul suggests, means finding the sum of 4 and -3, which is 1. So, Paul is correct that subtracting integers is equivalent to adding the opposite of the second number.
the length of the altitude drawn to the hypotenuse of right triangle t is 8. if the length of the hypotenuse of t is 20, what is the length of the shortest leg of t ?
The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.
We can start by using the area formula for a triangle:
Area = 1/2 * base * height
In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:
Area = 1/2 * c * h
Substituting the given values, we get:
Area = 1/2 * 20 * 8 = 80
We also know that T is a right triangle, so we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values, we get:
a^2 + b^2 = 20^2
a^2 + b^2 = 400
We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:
Area = 1/2 * base * height
80 = 1/2 * 20 * h
h = 8
a = (2 * Area) / c
a = (2 * 80) / 20
a = 8
Substituting a and h in the Pythagorean theorem equation, we get:
8^2 + b^2 = 20^2
64 + b^2 = 400
b^2 = 336
b = sqrt(336)
b ≈ 18.33
Therefore, the length of the shortest leg of T is approximately 18.33 units.
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Each month, Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars for his family. Crunchy granola bars come in boxes containing x bars, and chewy granola bars come in boxes containing y bars. Write two equivalent expressions for the total number of granola bars Tomas buys after 5 months. (5(__x+__y) and __x+__y)
The two equivalent expressions for the total number of granola bars Tomas buys after 5 months is 5(4x + 2y) and 20x + 10y
In mathematics, an expression is a combination of symbols (such as numbers, variables, and operators) that represent a mathematical object or value.
Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars each month. Let's assume that each box of crunchy granola bars contains x bars and each box of chewy granola bars contains y bars.
To express the total number of granola bars that Tomas buys in one month, we can use the following expression:
4x + 2y
This expression shows that Tomas buys 4 boxes of crunchy granola bars, each containing x bars, and 2 boxes of chewy granola bars, each containing y bars.
To find the total number of granola bars that Tomas buys after 5 months, we need to multiply the expression by 5, since he buys granola bars each month for 5 months. This gives us the expression:
5(4x + 2y) = 20x + 10y
Alternatively, we can also express the total number of granola bars that Tomas buys in 5 months using the following expression:
5x(4) + 5y(2) = 20x + 10y
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Here is the histogram of a data distribution.
LL
1
4 5 6 7 8 9 10
What is the shape of this distribution?
5
3
2-
OA. Bimodal
B. Unimodal skewed left
OC. Uniform
OD. Unimodal skewed right
OE. Unimodal symmetric
Answer:
A. Bimodal
Step-by-step explanation:
You want a description of the shape of the histogram shown.
ModeThe mode of a dataset is the value that appears most often. When two values have that distinction, the data is said to be "bimodal."
Here, the most a data item appears is 6 times. Two data items have that distinction: 2 and 7. Hence, the shape of the distribution is ...
A. Bimodal
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help asap pls. question in pic
the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
One side of rectangle is 200m
When the measure of the other side is 50 m
the area will be 50*200 = 1000m².
The expression of area A(x) = 200x,
hence the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
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What expression is equivalent to 24a+(-26b)-13a+12b?
The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".
Given expression ,
24a+(-26b)-13a+12b
= 24a - 13a +12 b - 26b
= 11a - 14b
Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
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A travel club can spend at most 10 nights in two cities on a trip. The club needs to reserve four rooms each night and wants to spend no more than 4200 on hotels and fuel. The estimated fuel cost is 200 can the club spend 3 nights in city a and 6 nights in city b? 7 nights in city a and 3 nights in city b? justify your answer using a system of linear equations
To solve this system, we must first determine the number of available rooms in each city, as well as the per-night cost of hotel rooms. Without that information, we can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B.
Let's start by defining the variables we'll need to solve this problem:
Assume that x is the number of nights spent in City A.
Let y represent the number of nights in City B.
To determine whether the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, we must first determine whether the total cost of hotels and fuel for each scenario is less than or equal to $4200.
Given that the estimated cost of fuel is $200, the cost of hotels must be less than or equal to $4000.
The following equations calculate the cost of hotels for each scenario:
3x + 6y = cost of hotels for spending 3 nights in city A and 6 nights in city B7x + 3y = cost of hotels for spending 7 nights in city A and 3 nights in city BWe also know that the club can only spend a total of 10 nights, so x + y must be less than or equal to 10.
Finally, we must ensure that the club can book four rooms each night. This means that the number of rooms required per night in each city is four times the number of nights. As a result, we must have:
4x ≤ number of available rooms in city A4y ≤ number of available rooms in city BWhen we combine all of these constraints, we get the following system of linear equations:
3x + 6y + 200 ≤ 4200 (cost constraint for spending 3 nights in city A and 6 nights in city B)
7x + 3y + 200 ≤ 4200 (cost constraint for spending 7 nights in city A and 3 nights in city B)
x + y ≤ 10 (total number of nights constraint) (total number of nights constraint)
A city with 4x available rooms (room constraint for city A)
4y rooms available in city B (room constraint for city B)
To solve this system, we must first determine the number of available rooms in each city as well as the cost of hotel rooms per night. We can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, without that information.
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At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain. How many cups of iced tea did people drink during the party?
Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.
To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.
One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to
7 * (1/16) = 7/16 quarts.
Thus, the total amount of iced tea that was consumed during the party is 912 quarts -
7/16 quarts = 912 - 7/16
= 912 - 7 * (1/16)
= (912 * 16 - 7 * 1) / 16
= 1476 / 16
= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.
It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.
In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to
92 * (1/4) = 23 quarts.
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the days to maturity for a sample of five money market funds are shown here. the dollar amounts invested in the funds are provided. days to maturitydollar value ($ millions) 1515 1110 725 515 410 use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. round your answer to decimal places. days
The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.
To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.
The calculation for the weighted mean is as follows:
Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)
where D represents the days to maturity and V represents the dollar value.
Using the given values, we can plug them into the formula and get:
Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)
Weighted Mean = 8.95 (rounded to two decimal places)
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A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4 Using this recipe 250g of syrup are needed to make 12 flapjacks find the quantity of oats needed to make 18 of these flapjacks?
A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4. Using this recipe 250g of syrup are needed to make 12 flapjacks. The quantity of oats needed to make 18 of these flapjacks is 375g.
The recipe for flapjacks has a ratio of syrup to sugar to butter to oats of 1:2:2:4. This means that for every 1 unit of syrup, there are 2 units of sugar, 2 units of butter, and 4 units of oats.
We know that 250g of syrup are needed to make 12 flapjacks. To find out how much oats are needed to make 18 flapjacks, we can set up a proportion:
syrup: sugar: butter: oats = 1:2:2:4
250g:x = 12:18
To solve for x, we can cross-multiply and simplify:
250g * 18 = 12x
4500g = 12x
x = 375g
Therefore, we need 375g of oats to make 18 flapjacks using this recipe.
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a car rental company offers two plans for renting a car: plan a: 30 dollars per day and 12 cents per mile plan b: 50 dollars per day with free unlimited mileage for what range of miles will plan b save you money for a 1 day rental? to save money the mileage must be greater than miles per day.
Plan B will save you money for a 1-day rental if you drive more than 166.67 miles.
To determine the range of miles for which Plan B will save money over Plan A for a 1-day rental, we need to set up an equation that compares the total cost of each plan.
For Plan A, the cost is given by:
Cost(A) = 30 + 0.12x
where x is the number of miles driven.
For Plan B, the cost is given by:
Cost(B) = 50
since there is no additional charge for mileage.
To determine the range of miles for which Plan B is cheaper than Plan A, we need to find the value of x for which:
Cost(B) < Cost(A)
Substituting the expressions for the costs of each plan, we get:
50 < 30 + 0.12x
Simplifying this inequality, we get:
0.12x > 20
x > 20 / 0.12
x > 166.67
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question 14
pls help me asap i am being timed
Answer:
164 degree is the answer
Answer:
Step-by-step explanation:
Chord PM and PN are equal
arc PM = arc PN
164=5x+4
x=32
arc PN = 5x+4 = 5(32)+4=164
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct? Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24. Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24. Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24. Zachariah and Khai have the same ratio of American stamps.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
What is a ratio?A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3).A ratio is a metric used to compare like-kind data or depict relationships between them. Ratios are used to contrast similar items. In your class, for instance, we might compare the ratio of boys to girls using that information.Usually by dividing them, ratios compare two numbers. Your formula would be A/B if you were comparing two different data points (A and B).To learn more about ratio refer to:
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How are the ordered pairs (,) and (,−) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
Answer: no exact answer
Step-by-step explanation:
[tex]\frac{-3x+6}{x-2}[/tex] = 0
solve for x. if there is no solution, write no solution.
Answer:
there is no solution
Step-by-step explanation:
Daniel was given a large box of 36 chocolates for his birthday. If he eats exactly 3
chocolates each day, how many chocolates would Daniel have remaining 8 days after
his birthday?
Answer:12
Step-by-step explanation:
8 times 3 equals 24.24 subtract36 get 12
What is the radius of a circle whose circumference measures 154 inches?
Answer: 77
Step-by-step explanation: to find the radius divide the circumference by 2.
Part 4: Fill in the blank. cos (56°) = sin(°)
The complete expression in the blank is cos (56°) = sin(34°)
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
cos (56°) = sin(°)
The blank expression can be calculated as
When x + y = 90;
sin(x) = cos(y)
Using the above as a guide, we have the following:
Blank + 56 = 90
Evakuate the like terms
Blank = 34
So, we have
cos (56°) = sin(34°)
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convert 26kg 45g into kg
Answer:
As 1000g=1 kg ⟹1g=
1000
1
kg.
26 kg 50 g.
=26 kg+50 g
=26 kg+50(
1000
1
)kg.
=26+0.05 kg.
=26.05 kg.
Answer: 26kg, 0.045kg
Step-by-step explanation:
What is the mode of the data set 0,0,1,1,1,2,2,2,2,3
Answer:
Step-by-step explanation:
2, there are 4, making it the most.
10 The number of students who brought
their own lunch to school on Tuesday was"
57 fewer than the number of students
who ate the school lunch. There were
more than 485 students who brought
their lunch.
Part A
Write an inequality to find the possible
number of students, n, who ate the
school lunch.
Part B
How many students could have possibly
eaten the school lunch?
Part A: The inequality to find the possible number of students, n, who ate the school lunch n > 542 students
Part B: The number of students, that possibly eat lunch at school is 542 or more students
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Part A; The number of students who bring lunch, B > 485 students
The number of students who eat lunch in school, E = B + 57
∴ E > 485 + 57
The number of students who can possibly eat lunch in school;
E > 542 students
Part B;
The number of students, n, that possibly eat lunch at school, are;
n = 542 or more students.
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How many terms are in this expression?
4n + 6m
Answer:
2
Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms
Find the approximate values of the five number summary for the data set represented by this box plot,
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
The Approximate values of the five number summary are ;
(i) the Minimum is 10 ,
(ii) the First quartile is 30 ,
(iii) the Third Quartile is 80 ,
(iv) the Median is 55 ,
(v) the Maximum is 100 .
The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .
(i) the Minimum of the data set is = 10 ;
(ii) we split the data set into , 2 halves ;
that means ; {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } ;
So , first quartile (Q₁) = 30 ;
(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
So , Q₃ = 80 ;
(iv) the total number of terms in the set is = 19 ;
So , the median is = tenth term = 55 ;
(v) the maximum of the data set is = 100 .
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Here is a histogram showing
the times taken to complete
a task.
Estimate the percentage of
people who took less than
30 seconds to complete
the task.
Give your answer to
1 decimal place. Frequency
The percentage of people who took less than 30 seconds to complete
the task 84.4%.
The diagram shows us how many people finished the task in what time.
40 people finished in 5-10 seconds.
40 people finished in 10-15 seconds.
30 people finished in 15-20 seconds.
30 people finished in 20-25 seconds.
25 people finished in 25-30 seconds.
25 people finished in 30-35 seconds.
25 people finished in 35-40 seconds.
25 people finished in 40-45 seconds.
15 people finished in 45-50 seconds.
That is what the diagram is telling us, and what "frequency" means in this case.
Therefore,
In total, 255 people participated.
only the last 2 groups took longer than 40 seconds.
Therefore,
The estimate of how many took less than 40 seconds is
255 - 25 - 15 = 215 people.
215 people are how many % of 255 :
100% = 255
1% = 100%/100
= 255/100
= 2.55
215 is a many % as how often 1% fits into these 215 :
215 / 2.55 = 84.31372549%
≈ 84.4%
Complete Question:
Times taken to complete a task. Here is a histogram showing the times taken to complete a task.
40- Estimate the percentage of 35 people who took less than 40 seconds to complete the task.
Give your answer to 1 decimal place.
Frequency Density : 1 5 0 5
Time (Density) :
10 15 20 25 30 35 40 45 50
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scores on a certain test are normally distributed with a variance of . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than units.
A sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units.
To find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, we can use the formula:
n = [ (z * σ) / E ]^2
where n is the required sample size, z is the critical value for the desired confidence level (95% confidence level corresponds to a z-value of 1.96), σ is the population standard deviation (given as the square root of the variance, which is √(70) ≈ 8.37), and E is the maximum error, or the maximum difference between the sample mean and population mean that we are willing to tolerate (which is given as 2.5 units).
Substituting the given values into the formula, we get:
n = [ (1.96 * 8.37) / 2.5 ]^2
n ≈ 43.48
Rounding up to the nearest whole number, we get a required sample size of n = 44.
Therefore, a sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, assuming a normal distribution with a population variance of 70.
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scores on a certain test are normally distributed with a variance of 70 . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2.5 units.
