An expression is defined as a set of numbers, variables, and mathematical operations. The total number of students is 54.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the number of columns in the rollercoaster be represented by x.
If students sit 4 per row on a rollercoaster, 6 students are left without a seat. Therefore, the number of students can be written as,
Total number of students = 4x + 6
If they sit 6 per row, there are 3 rows left empty. Therefore, the total number of students can be written as,
Total number of students = 6(x-3)
The total number of students can be written as,
4x + 6 = 6(x - 3)
4x + 6 = 6x - 18
2x = 24
x = 12
Now, the total number of students in the class are,
4x + 6 = 4(12) + 6 = 54
Hence, the total number of students are 54.
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The graph of the function f(x) = (x-3)(x + 1) is shown.
-10-8-6
q
10-
Which describes all of the values for which the graph is
positive and decreasing?
all real values of x where x < -1
all real values of x where x < 1
all real values of x where 1
O all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Draw a parabola (the graph) passing trough two x-intercepts -1 and 3 and open up.
Where would 8.46 be located on a number line?
8.46 be located between 8.45 and 8.47 on a number line.
What is the number line?A number line is a horizontal line that has equally unfolded range increments. The numbers protected on the line will determine how the wide variety on the road may be responded to. The query that goes with the wide variety determines how it will likely be used, as an instance, in plotting a point.
What is a number line example?Numbers on various lines include all sets of numbers namely natural and complete numbers. An instance of a fixed of entire numbers is:(0, 1, 2, 3,5,6 …….) while the natural numbers consist of:1, 2, 3, four, five, 6…. a number of lines consists of 3 basic elements. within the center, the starting place is commonly plotted with 0.
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What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)²+3?
Answer: 3
Reason:
Going from x^2 to (x+5)^2 means we shift the graph 5 units to the left.
The +3 at the end shifts the parabola up 3 units. This is because we add 3 to each y value. For instance a point like (0,25) moves to (0,28)
The courthouse is the tallest building in the city. If it is 71/2 6 inches tall in the model, how tall is the actual building?
The actual height of the building is 67 1/2 feet
Complete questionThe courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?
Scale factor: 1 inch = 9 feet
How to determine the actual height?The given parameters are:
Scale height = 7 1/2 inchesScale factor: 1 inch = 9 feetThis means that:
7 1/2 inches : Actual = 1 inch = 9 feet
So, we have:
Actual =7 1/2 * 9 feet
Evaluate the product
Actual = 67 1/2 feet
Hence, the actual height of the building is 67 1/2 feet
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Please help meeeeeeeeee???
The answer for the exponential expressions 1,2,3 and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.
What exactly is an exponent?Exponential notation is a type of mathematical shorthand that allows us to write complex formulas in a more concise manner.
The basis of an exponent is a number or letter. It means that the base will be raised to a given level of power. The base is X, and the power is n.
The properties of the exponent used;
[tex]\rm m^a \times m^b = m^{a+b} \\\\ m^a \times n^a = {mn}^a \\\\ m^a \times m^b = m^{a-b} \\\\ m^0 = 1[/tex]
Expression 1;
[tex]\frac{(2.3^{-2})^2(5.3^2.2)^2}{(3)^-2(5.2)^2} \\\\ \frac{2^3.3^{-6}.5^2.3^6}{3^{-2}.5^2.2^2} \\\\ 4.5[/tex]
Expression 2;
[tex](3^3)(4^0)(3.2)^{-3}(2)^2 \\\\ 3^3.1.3^{-3}.2^{-3}.2^2 \\\\ \frac{1}{2}[/tex]
Expression 3;
[tex]\frac{(3^7.4^7)(2.5)^{-3}(5)^2}{12^7.5^{-1}.2^{-4}} \\\\ \frac{3^7.4^7.25^{-3}.5^{-3}.5^2}{12^7.5^{-1}2^{-4}} \\\\ 2[/tex]
Expression 4;
[tex]\frac{(2.3)^{-1}.2^0}{(2.3)^{-1}}\\\\ \frac{2^{-1}.3^{-1}.1}{2.3}\\\\ 1[/tex]
Hence, the answer for the exponential expressions 1,2,3, and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.
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Choose the end behavior of the graph of each polynomial function.
Options
Falls to the left and rises to the right
Rises to the left and falls to the right
Rises to the left and rises to the right
Falls to the left and falls to the right
Using limits, the end behavior of the functions are given as follows:
a. Rises to the left and falls to the right.
b. Rises to the left and rises to the right.
c. Falls to the left and rises to the right.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In item a, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]
Hence it rises to the left and falls to the right.
In item b, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]
Rises to the left and rises to the right.
In item c, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]
Falls to the left and rises to the right.
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1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.
A) Not binomial: there are too many trials.
B) Procedure results in a binomial distribution.
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: the trials are not independent.
The 15 are women, keeping track of the number of men chosen is Not binomial the trials are not independent.
We have given that,
The given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.
What is the Binomial distribution?In samples with replacement, the probability has to be the same for each trial, that is, they are independent.
Hypergeometric distribution
Samples without replacement, as the probabilities depend on the previous outcomes, that is, they are not independent.
In this question
Marbles are chosen without replacement, which means that for each trial the probabilities of choosing a red marble are different, which means that the trials are not independent. So the answer is:
Not binomial the trials are not independent.
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. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2)
Answer:
12
Step-by-step explanation:
Input interpretation: triangle | vertex coordinates (-3, 5) | (-3, 2) | (1, 2) | perimeter
Result: 12
Properties of Triangle:
edge lengths | 3 | 4 | 5 area | 6perimeter | 12interior angles | (cos^(-1)(4/5) rad | cos^(-1)(3/5) rad | π/2 rad)≈(0.643501 rad | 0.927295 rad | 1.5708 rad)interior angle sum | 180° = π rad≈3.142 radwhich choice is equivalent to the expression below? square root of -64
Step-by-step explanation:
[tex] \sqrt{ - 64 } = - 8[/tex]
so the answer you got pls mark branlist
One third of a number less than nine equal to seven
12. Allison is buying some boxes of frozen treats: popsicles, p, ice cream bars, b, and ice cream
sandwiches, s. All three items cost $2.25 for each box. Write two equivalent expressions to
determine how much Allison will spend on all the frozen treats.
Answer:
One possible answer is: 2.25p + 2.25b + 2.25s
Another possible answer: 2.25(p + b + s)
==========================================================
Explanation:
p = number of popsiclesb = number of ice cream barss = number of ice cream sandwichesEach item costs $2.25 per box, so,
2.25p = cost of just the popsicles only2.25b = cost of just the ice cream bars only2.25s = cost of just the ice cream sandwiches onlyAdd up those subtotals to get the grand total
2.25p + 2.25b + 2.25s
is one possible answer
What we can do is factor out the common 2.25 using the distributive rule in reverse.
Another possible answer is: 2.25(p + b + s)
Which statement is true about the information in the double line graph?
A. The number of customers at 12:00 was less on Friday than Saturday.
B. There were more customers on Saturday than Friday.
C. The number of customers was less Saturday than Friday at 10:00 a.m. because many customers slept later.
D. The highest number of customers on both days was at 12:00 p.m.
Answer:
the answer is d as 38 31 which are highest
Step-by-step explanation:
a is false as 38>31 which is on Saturday
b is false as Saturday customers were less we can infer from the last three on Friday
c false as Saturday was 12 people and Friday 6 people
Write g(f(x)) as an expression in terms of x
An expression is defined as a set of numbers, variables, and mathematical operations. The value of g(f(x)) is (x²-10x+13) / (x²-10+29).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The complete questions is,
Write g(f(x)) as an expression in terms of x
f(x) = x-5
[tex]g(x) = \dfrac{x^2-12}{x^2+4}[/tex]
The value of g(f(x)) as an expression in terms of x can be written as,
[tex]g(f(x)) = \dfrac{(x-5)^2-12}{(x-5)^2+4}\\\\\\g(f(x)) = \dfrac{x^2+25-10x-12}{x^2+25-10x+4}\\\\\\g(f(x)) = \dfrac{x^2-10x+13}{x^2-10+29}[/tex]
Hence, the value of g(f(x)) is (x²-10x+13) / (x²-10+29).
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C
7 cm
D
What is the sum of the areas of circle C and circle D?
O 7π units²
O 14π units²
O49π units²
O 98π units²
Answer:
[tex]98 \pi \:\: \sf units^2[/tex]
Step-by-step explanation:
[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
From inspection of the given diagram, circle C and circle D both have a radius of 7 cm.
Therefore:
[tex]\implies \textsf{Area of circle C}=\pi (7)^2=49 \pi \:\: \sf cm^2[/tex]
[tex]\implies \textsf{Area of circle D}=\pi (7)^2=49 \pi \:\: \sf cm^2[/tex]
Therefore, the sum of the areas of circle and circle D is:
[tex]\implies \textsf{Area of circle C}+\textsf{Area of circle D}=49 \pi + 49 \pi = 98 \pi \:\: \sf cm^2[/tex]
The sum of the areas of the circles is 98π units².
The correct option is D.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
The formula for the area of a circle is A=πr², where A is the area and r is the radius.
For circle C, the radius is 7, so its area is A_C = π(7)² = 49π units².
For circle D, the radius is also 7, so its area is A_D = π(7)² = 49π units².
The sum of the areas is therefore:
A_C + A_D = 49π + 49π = 98π units²
Therefore, the answer is (D) 98π units².
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If the scale of a map is 1 cm : 2500m . The distance between two places in real field is 15 km . What is the distance between the places in map?
Answer:
To find out actual distance on earth, we need to measure scale. The scale is 1cm to 15 km. Thus, 10 cm on map is equal to ( 10*15) = 150 km on earth. Thus, actual distance on earth is 150 km.
Who is credited with creating an alphabet for several Slavic languages?
Answer:
the credit goes to create slavic language isSt. Cyril (or Constantine) and St. Methodius.
St. Cyril ( or Constantine) and St. Methodius are credited with creating an alphabet for several Slavic languages.
Here,
We have to find, Who is credited with creating an alphabet for several Slavic languages.
Who was Slavs?
Slavs are Indo-European people who speak the various Slavic languages of the larger Balto-Slavic linguistic group.
Now,
St. Cyril ( or Constantine) and St. Methodius are credited for creating an alphabet for several Slavic languages.
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Which function has an x-intercept of - 4 and a y-intercept of 3 when graphed?
The function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3
Intercepts of a lineThe x-intercept of a line is the point where the line crosses the x-axis while the y-intercept of a line is the point where the line crosses the y-axis.
For the x-intercept, y = 0
For the function f(x) = 3/4x + 3
0 = 3/4x + 3
0 = 3x + 12
-3x = 12
x = -4
This shows that the function has an x-intercept of -4
For the y-intercept, x = 0
For the function f(x) = 3/4x + 3
y = 3/4(0) + 3
y = 3
This shows that the function has an y-intercept of 3
Hence the function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3
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What is the slope of = -x +7 ?
Answer:
I assume you meant "y = -x+7" not "= -x +7". If that is correct then the slope is -1.
Step-by-step explanation:
The slope is the coefficient of the x in slope-intercept form. Therefore, the slope is -1.
Please give me Brainliest if this answer is correct.
An IV solution of 120 mL at a drip rate of 5 gtt/min using a tubing factor of 20 gtt/mL has been ordered to be initiated at 1545. Calculate the infusion time. (Round your answer to the nearest tenth of an hour.
The infusion time for the IV solution that will be prescribed 480 mins.
What is IV infusion time?The time taken by the saline to be dripped in the infusion is called as the infusion time.
To calculate the infusion time the formula for IV drip rate is used which is;
Drip rate = volume/time × Drop factor
Drip rate = 5gtt/min
Volume = 120mL
Drop factor= 20 gtt/mL
Time = ?
From the formula above, make time the subject of the formula. That is,
Time = vol × drop factor/drip rate
Time = 120 × 20/5
Time= 120 x 4
Time= 480 mins
Therefore, the infusion time for the IV solution that was prescribed = 480 mins
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Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
1f(x) = x(x-a)²(x - b)4
2f(x) = x(x - a)³(x- b)²
3f(x) = x²(x-a)(x- b)²
4f(x) = x²(x-a)5(x- b)
The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)² with four turning points
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
Hence the polynomial represented by the graph is of degree 5 since it has 4 turning points. The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)²
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A _______ random variable has infinitely many values associated with measurements.
Answer:
continuous random variable
please I need the answer :-)
Answer:
Step-by-step explanation:
Which statements are true about the linear inequality y > three-fourthsx – 2? select three options.
The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
What is linear inequality?Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.
Using the general formula for linear inequality,
y >mx+ b
y > 3/4x - 2
Where m = slope of the graph
b = interception at y axis
Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
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What is the vertex of the graph of the function below?
y=x² + 4x-6
A. (2,0)
B. (-2,6)
C. (-2,-10)
D. (2,6)
The total debt that frances carries is $2,355 and she has a total credit limit of $5,000; her partner jeremy has a total debt
of $3,465 and his total credit limit is $8,000.
find frances' debt-to-credit ratio. express this ratio as a decimal. round to the nearest thousandth.
then find jeremy's debt-to-credit ratio. express this ratio as a decimal. round to the nearest thousandth.
who has the higher debt-to-credit ratio? (frances or jeremy)
Jeremy's debt-to-credit ratio is 0.471.
What is debt-to-credit ratio?debt-to-income ratio is the percentage of a consumer's monthly gross income that goes toward paying debts.
Here, Based on the given conditions,
formulate = Total debt / total credit limit
= 2355 / 5000
= 471/1000
Cross out the common factor: 471/1000
Round 471/1000 to the required place:: 0.471
Thus, Jeremy's debt-to-credit ratio is 0.471.
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Someone please help with this ::
Answer:
pi/6
Step-by-step explanation:
honestly just do it in a calculator that is set to radians.
Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Jaime is incorrect, the angle does not depend on the radius of the circles.
Is Jaime correct?Remember that an angle that defines an arc on a circle, does not depend on the radius of the circle.
So, if we have an angle with a measure of π/3 radians in a circle with a radius of 3 inches and an angle with a measure of π/3 radians in a circle with a radius of 6 inches, these two angles are exactly the same thing.
The radius of the circle only has an impact on the length of the arc defined by the angle.
So Jaime is clearly incorrect.
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2x - 8≤ -10
please find the value of x.
SHOW WORK IF POSSIBLE
Answer:
x ≤ - 1
Step-by-step explanation:
2x - 8 ≤ - 10 ( add 8 to both sides )
2x ≤ - 2 ( divide both sides by 2 )
x ≤ - 1
Answer:
x ≤ -1
Step-by-step explanation:
Given,
2x - 8≤ -10
Solution:
Add 8 to both sides:
2x-8+8≤-10+82x≤-2Divide both sides by 2:
2x/2 ≤ -2/2x ≤ -1Value of x is ≤ -1.
Find the value of the following:
1. Decrease 1.25km by 0.6%
2. Decrease 64 g by 12 ½%
3. Decrease 124 L by 15%
4. Decrease 350m² by 42%
Step by step working please!
The required decreased value is given by 1.2425, 56g, 105.4L, 203m²
What are percentage?
percentage is the ratio of composition of matter to the overall composition of matter multiplied by 100.
1) Decrease 1.25km by 0.6%
0.6% of 1.25km = 0.0075
so total decrease = 1.25 - 0.0075
= 1.2425
similarly,
2.) Decrease 64 g by 12 ½%
12 ½% of 64g = 8g
so total decrease = 64-8
= 56g
3. Decrease 124 L by 15%
15% of 124 = 18.6L
so total decrease = 105.4L
4. Decrease 350m² by 42%
42% of 350m² = 147m²
so total decrease = 203m²
Thus, the required decreased value is given by 1.2425, 56g, 105.4L, 203m²
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Calculate the difference in the proportion of males and the proportion of females that smoke. Give your answer to 2 decimal places
The difference in the proportion of males and the proportion of females that smoke is 0.08
Missing informationIn a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.
How to determine the proportion difference?The given parameters are:
Male Female
Sample 61 48
Smokers 15 8
The proportion is calculated using:
p = Smoker/Sample
So, we have:
Male = 15/61 = 0.25
Female = 8/48 = 0.17
The difference is then calculated as:
Difference = 0.25 - 0.17
Evaluate
Difference = 0.08
Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08
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