Jeriel pays $75 for an additional 2 GB of data, and 45+15x for every further 1 GB of data.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
Here,
For 6 GB, the cost is $45.
For per GB extra the cost is $15.
The cost of data paid by Jeriel,
=45+2*15
=$75
For x GB, the cost is,
=45+15x
The cost of data paid by Jeriel for 2 GB extra data is $75 and for x GB, the cost paid is 45+15x.
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Find the x-intercept of the line 8x+8y=–
1
Answer:
x-intercept is [tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
The x-intercept is the Value of x when y = 0
So for our Equation , 8x + 8y = -1
At y = 0 , 8x + 0 = -1
Then 8x = -1
Then x = -1/8
Two buildings are 18.5 meters apart. The angles of elevation from the top of one building to the top of the other is 18 degrees. If the taller building is 15 meters tall, how tall is the shorter building?
Find the domain and solve. screenshot included
The domain of the expression [tex]{\frac{1}{4} }^{\frac{2-x}{x} } > 64^{2}[/tex] is
-∞ < x < 0; 0 < x < ∞The solution of the equations is
x < -2/5How to find the domainThe domain of a function is all possible input values of the function
for a fraction the denominator should not be zero. therefore
In the function given: (2 - x) / x in this case x ≠ 0
The domain is then all numbers excluding 0, (-∞, 0) U (0, ∞)
The equation is solved as follows
[tex]{\frac{1}{4} }^{\frac{2-x}{x} } > 64^{2}[/tex]
solving to have a common base
[tex]4^{-1\frac{2-x}{x} } > (4^{2}) ^{3}[/tex]
[tex]4^{-\frac{2-x}{x} } > 4^{6}[/tex]
equating the bases
[tex]{-\frac{2-x}{x} } > 6[/tex]
-2 + x > 6x
-2 > 6x - x
-2 > 5x
-2/5 > x
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A box contains 4 pears and 7 oranges. Three fruits are taken out at random and eaten. Find the
probability that
(1) 2 pears and 1 orange are eaten, in any order,
(ii) the third fruit eaten is an orange,
(iii) the first fruit eaten was a pear, given that the third fruit eaten is an orange.
(i) The probability that 2 pears and 1 orange are eaten in any order is equal to [tex]\frac{14}{55}[/tex]
(ii) The probability that the third fruit eaten is an orange is equal to [tex]\frac{7}{15}[/tex]
(iii) The probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to [tex]\frac{6}{11}[/tex]
What is Probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. It is more likely that an event will occur if its probability is higher.For example, the probability of tossing a coin and getting a head is equal to [tex]\frac{1}{2}[/tex]What are Combinations?
Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.The formula for calculating the number of alternative configurations by picking only a few items from a set of objects with no repetition is written as follows in mathematics, [tex]{n \choose k }=\frac{n!}{k!(n-k)!}[/tex]Here, it is given that the box contains 4 pears and 7 oranges in the box.
So, the total number of fruits in the box = 4 + 7 = 11
Combination when 2 pears is chosen out of 4 pears from the box [tex]= {4 \choose 2} = \frac{4!}{2!(4-2)!} =6[/tex]
Combination when 1 orange is chosen out of 7 oranges from the box [tex]= {7 \choose 1} = \frac{7!}{1!(7-1)!} =7[/tex]
Combination when 2 pears and 1 oranges are taken from the box containing a total of 11 fruits [tex]= {11 \choose 3} = \frac{11!}{3!(11-3)!} =165[/tex]
So, the probability that 2 pears and 1 orange are eaten, in any order,
[tex]P(A) =\frac{ {4 \choose 2} \times {7 \choose 1} }{ {11 \choose 3} } \\\implies P(A) = \frac{6 \times 7}{165} \\\implies P(A) = \frac{14}{55}[/tex]
Now, the probability that the third fruit eaten is an orange is given as,
[tex]P(B)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}+{1 \choose 7}{1 \choose 6}{1 \choose 5}}{A(11,3)} \\P(B)=\frac{460}{990} \\P(B)=\frac{7}{15}[/tex]
Next, we can find the probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is a conditional probability problem where one event depends on another event.
The probability that the third fruit is orange P(A) is equal to 7/15
The probability that the first fruit eaten was a pear is calculated as,[tex]P(C)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}}{A(11,3)} \\P(C)=\frac{252}{990} \\P(C)=\frac{14}{55}[/tex]
So, according to conditional probability,
Probability of C given A,
[tex]P(C/A)=\frac{P(C \cap A)}{P(A)} \\\implies P(C/A)=\frac{\frac{14}{55} }{\frac{7}{15} } \\\implies P(C/A)=\frac{6}{11}[/tex]
There, the (i) probability that 2 pears and 1 orange are eaten in any order is equal to [tex]\frac{14}{55}[/tex]
(ii) probability that the third fruit eaten is an orange is equal to [tex]\frac{7}{15}[/tex]
(iii) probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to [tex]\frac{6}{11}[/tex]
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A mill uses 4 times as much power as a lathe. If the total power used by a mill and 3 lathes is 1540 kilowatts, find the power used by a single lathe.
Answer:
Step-by-step explanation
Answer:
220 kW
Step-by-step explanation:
You want the power used by a single lathe when a mill uses 4 times as much, and a mill plus 3 lathes uses 1540 kW.
SetupLet p represent the power used by a single lathe. Then a mill uses 4p, and the given total is ...
(4p) +3p = 1540
Solution7p = 1540 . . . . . . collect terms
p = 220 . . . . . . . divide by 7
A single lathe uses 220 kW.
if 2=394.76366368379232
then how much would
938738393x2+8732893673-8238339x2=
Answer:
Following is a very common example of calculating Sales Commission based on levels of Reven…
•=IF(C9>15000,20%,IF(C9>12500,17.5%,IF(C9>10000,15%,IF(C9>7500,12.5%,IF(C9>5000,10%,0))…
This formula says IF(C9 is Greater Than 15,000 then return 20%, IF(C9 is Greater Than 12,500 th…
While it’s remarkably similar to the earlier Grades example, this formula is a great example of how difficult it can be to maintain large IF statements – what would you need to do if your organization decided to add new compensation levels and possibly even change the existing dollar or percent
Step-by-step explanation:
Find the missing length indicated.
Answer:
14 unitsStep-by-step explanation:
Let the missing part be x.
According to triangle proportionality theorem we have:
x/28 = 6 /(18 - 6)x = 28*6/12x = 14The missing length will be 14 units.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown is figure.
Now,
Let the missing length = x
So, By the definition of triangle proportionality theorem, we get;
⇒ x/28 = 6 /(18 - 6)
Solve for x as;
⇒ x/28 = 6 /(18 - 6)
⇒ x/28 = 6 / 12
⇒ x/28 = 1 / 2
⇒ x = 28/2
⇒ x = 14
Thus, The missing length will be 14 units.
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On a map of texas, the cities of midland, lubbock, and odessa form a triangle. Midland is 20 miles from odessa, and lubbock is 113 miles from midland. What is the farthest, in miles, odessa could possibly be from lubbock?.
The shortest possible distance in miles between Odessa and Lubbock is 114.75 miles
Given information;
The cities of Midland, Lubbock, and Odessa make a triangle on a Texas map. Odessa is 20 miles away from Midland, and Lubbock is 113 miles away.
What is the shortest possible distance in miles between Odessa and Lubbock?
It states that a triangle is formed and the required distance is the farthest one.
So, for a triangle applying the hypotenuse theorem can solve the case,
The theorem states that the sum of the squares of the two sides is equal to the square of the other side.
D² = 20² + 113²
D² = 400 + 12769
D² = 13169
D = √13169
D = 114.75
Therefore, Odessa could be 114.75 miles from Lubbock.
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PLEASE HELP GEOMETRY 20 POINTS
Answer:
fourth option
Step-by-step explanation:
The largest angle in the triangle is opposite the longest side
The smallest angle in the triangle is opposite the shortest side
largest side is WX = 14
shortest side is VW = 9
then smallest to largest angles are
∠ X , ∠ W , ∠ V
How do I solve a 1 2bh?.
To solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
What is the area of the triangle?
In a two-dimensional plane, the area of a triangle is the region enclosed by it. As we all know, a triangle is a closed shape with three sides and three vertices. Thus, the area of a triangle is the total space occupied by the triangle's three sides. The general formula for calculating a triangle's area is half the product of its base and height.
The given formula is 1/2bh
so this is the formula for finding out the area of the triangle where 'B' is the base of the triangle and H is the height of the triangle.
To solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
Hence, to solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
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(100 POINTS AND BRAINLIEST)
An electric toothbrush costs $69, including a 50% price markup. What was the cost for the store to purchase the electric toothbrush?
Answer:
The cost of the electric toothbrush is the $34.
Step-by-step explanation:
We have to find that the cost for the store to purchase the electric toothbrush.
cost of the electric toothbrush = $69 - 50% of $69
cost of the electric toothbrush = $69 - 50/100* 69
cost of the electric toothbrush = $69 - 34.5
cost of the electric toothbrush = 34.5.
Calvin states that it is not possible to find the equation of a line
parallel to y=2 and passing through the point (5,-1) using the
point-slope form because the equation of the line does not have
an x-term. Explain the error in Calvin's reasoning.
The equation of a line y = 2 in point-slope form can be written as
(y + 1) = 0(x - 5).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, An equation of a line y = 2 which is a line parallel to the x-axis at
y = 2.
As it is parallel to the x-axis the slope of the line is zero passing through points (5, - 1).
The equation of a line in point-slope form is (y - y₁) = m(x - x₁).
∴ (y + 1) = 0(x - 5).
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A forest ranger wants to do a survey to check the general health of the trees in their care. These are:
Oak 50
Beech 40
Walnut 10
Pine 80
Spruce 20
They have enough time to survey 40 trees, and they want to do a stratified survey. How many trees are there? How many oaks should they survey? How many pines should they survey?
There are a total of 200 trees in the forest ranges and there are 50 oak trees while there are 80 pine trees.
What is a frequency table?A frequency table lists a group of values along with how frequently each one occurs. The frequency of a given data value in your dataset is the number of times it appears. These tables assist you in determining which data values are typical and which are uncommon.
It is given that the data in the table,
Oak 50
Beech 40
Walnut 10
Pine 80
Spruce 20
Thus, there are a total of 200 trees in the forest ranges and there are 50 oak trees while there are 80 pine trees.
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The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1,536 cm2, find the dimensions (in cm) of the poster with the smallest area.
The dimensions of the poster with the smallest area are = 64cm X 56cm where Width of the poster is 64 and Height of the poster is 56.
In order to establish a condition equation that represents the printed area's width (w) in terms of its height (h), we must first use what we know about the printed area.
Ap(w,h)=wh [Printed area]
Ap(w,h)=wh [ Substitute Ap(w,h)=1536]
1536=wh
w=1536h [width ''w'' in terms of height ''h'' ]
The smallest surface area must be determined. We need to find out the area as a function of the variable h using the condition equation.
W=w+16 [ Width of the rectangular poster ]
H=h+24 [ Height of the rectangular poster ]
Ar(w,h)=(w+16)(h+24) [Area of the rectangular poster ]
Ar(w,h)=(w+16)(h+24)
Put the value of W in terms of ‘h’ that we got above.
Ar(w)=(1536h+16)(h+24)
Ar(w)=36864h+16h+1920
Ar(w)=36864/w+16w+1920 (objective function)
Determine the domain of objective function
D={w∈R:w>0} [Domain of the Objective area function]
Ar(w)=36864/w+16w+1920
A′r(w)=−36864w2+16 [First derivative of the Objective area function]
A′r(w)=0 [critical point condition]
−36864/w2+16=0
16=36864/w2
w2=36864/16
w2=2304
w=±48
w=−48 [w=−48∉D]
w=48 [w=48∈D]
w=48 [Critical point of the Objective area function ]
Applying sufficient condition for extremes (Second derivative test)
A′r(w)=−36864/w2+16
A′′r(w)=73728/w3[Second derivative of the Objective area function]
A′′r(48)=0.6 [A′′r(48)>0]
w=48 [Minimum point of the Objective area function ]
Calculate the dimensions of the rectangular poster with minimum area
w=48 Width of the print area
h=1536/48=32 (Height of the print area)
W=48+16=64 (Width of the rectangular poster)
H=32+24=56 (Height of the rectangular poster)
The dimensions of the poster with the smallest area are: ⟹64cm×56cm
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Alyssa has saved 4700 cents from selling lemonade.
How many dollars does Alyssa have?
Answer: 47 dollars
Step-by-step explanation: 100 cents makes a dollar 4700/100= 47
which statement is not true about nonresponse issues in sampling? increasing the response rate may not reduce nonresponse bias. response rates themselves do not indicate whether the respondents are representative of the original sample. nonresponse error is one of the most significant problems in survey research. for a given study, if the nonrespondents differ from the respondents on the characteristics of interests, the sample estimates will only be mildly biased.
Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
What is sampling?A statistical technique called sampling uses a small portion of a larger population to represent the entire population. Sampling is a topic that takes into account the many approaches that might be used to survey a segment of the population and looks for a sample that is most representative of the entire population. The ability of a particular subset of a population's members to be generalized to the entire population is referred to as a sample's "generalizability," or "representativeness." For a highly generalizable outcome,Sampling is a key tool in the scientific method, allowing researchers to provide evidence that generalizable theories are true simply from a sample of specific facts.Hence,Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
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Albert has y stickers.
Latika has more stickers than Albert.
John has times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
The algebraic expression, in terms of y , for the number of stickers John has is given by 4(y + 2)
How to write algebraic expression?Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Number of stickers Albert has = yNumber of stickers Latika has = y + 2Number of stickers John has = 4(y + 2)The expression for the number of stickers John has = 4(y + 2)
For instance, if y = 3
Number of stickers Latika has = y + 2
= 2 + 2
= 4 stickers
Number of stickers John has = 4(y + 4?2)
= 4(3 + 2)
= 4(5)
= 20 stickers
Therefore, the expression which can be used to represent the number of stickers John has is 4(y + 2)
Complete question:
Albert has y stickers.
Latika has 2 more stickers than Albert.
John has 4 times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
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Evaluate:
Tan(cos^-1(x/4))
The trigonometric function tan(cos⁻¹(x/4)) evaluates to √(16 - x²) / x
To evaluate a trigonometric function?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Given the trigonometric function tan(cos⁻¹(x/4)) to evaluate:
tan(cos⁻¹(x/4))
Let θ = cos⁻¹(x/4)
Thus, cos θ = (x/4) (remember: cos θ = adjacent/hypotenuse)
We can use this information to draw a right-angled triangle as shown (image attached). Considering the triangle:
4² = x² + y²
y² = 16 - x²
y = √(16 - x²)
That means, the opposite is y = √(16 - x²)
tan θ = y/x = √(16 - x²) / x (Since tan θ = opposite/adjacent)
tan(cos⁻¹(x/4)) = √(16 - x²) / x
Therefore, tan(cos⁻¹(x/4)) evaluates to √(16 - x²) / x
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Learn more
f(x) = 3x+2
What is f(5)?
NOW DUE AT 2:00PM !!!!!!!
Solve.
34.2 = 13.4 + 9.6x
Enter your answer as a mixed number in simplest form in the box.
Answer:
21 and 167/1000
"/" represents a fraction, so 167 over 1,000
Step-by-step explanation:
Hard to explain.
Answer: 2 1/6
Step-by-step explanation:
34.2 = 13.4 + 9.6x
34.2-13.4=9.6x
20.8=9.6x
20.8 divided by 9.6= 2.166666666
2 1/6
a solid cube of side length 11 is removed from each corner of a solid cube of side length 33. how many edges does the remaining solid have?
Answer:
After taking cubes from each corner,no edge will
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining 30 squares, how many grains of wheat should be placed on square ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
The number of grains on square 13 will be 4096 grains.
How to calculate the number of grain?No. of grains on the first square = 1 = 2^0
No. of grains on the second square = 2 = 1*2 = 2¹
No. of grains on the third square = 4 = 2*2 = 2²
No. of grains on the fourth square = 8 = 2*4 = 2³
From the pattern it could be seen that amount of wheat is doubled for every next square
So, the number of grains in the nth square = 2^n-1
Therefore, No. of grains on 13th square
= 2^13 -1
= 4096
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Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the left.
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
Mark this and return
The correct answer to inequality is option A .
What is inequality equation?
The mathematical expressions with inequalities area unit those with unequal sides on each side.
Main body:
For this case we have the following inequality:
-4(x+3)≤ -2 -2x
Applying distributive property on the left side we have:
-4x - 12≤ -2 -2x
Adding 2x to both sides of the inequality we have:
-4x +2x -12 ≤-2
-2x-12≤-2
Adding 12 to both sides of the inequality we have:
-2x-12 +12≤ -2 +12
Dividing by 2 to both sides of the inequality:
-2x ≤ 10
Multiplying by -1 on both sides, taking into account that the sense of inequality changes:
x≥ -10/2
x ≥ -5
hence, the solutions are given by all values greater than or equal to -5.
so , option A is correct.
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If f(x) = -2x + 12, find f(6).
The function f(x) = - 2 · x + 12 evaluated at x = 6 has an output equal to 0.
How to evaluate a linear function
Functions are have three features: Input, relation, output. The input is the independent variable, generally known as x, the relation is how the input and output are related, the output is the dependent variable, generally know as y.
In this problem, we should substitute on the input, make all algebraic operations associated to the relation and determine the variable within the output.
The procedure is now shown:
First, substitute on the input:
x = 6
y = - 2 · 6 + 12
Second, make the algebraic operations involved in the relation:
y = - 2 · 6 + 12
y = - 12 + 12
Third, determine the value within the output.
y = 0
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Jacob is a long-distance runner. His race is 10,000m. How far is the distance in miles?
Answer:
10000 meters = 6.214 miles
About 6 miles
Step-by-step explanation:
Soultion: How many meters are in a mile?
1600 meters: roughly 1 mile or 4 laps around the track.
Answer: 6.214
Please help me thank u very much
Answer:
y=-6
Step-by-step explanation:
this is because y equal to 7 is flat so for it to be parallel the other line also has to be flat so the line will be passing through the same y value for the entire time which is -6
Hopes this helps pleae mark brainliest
Write each fraction or mixed number as a decimal.
Use bar notation if the decimal is a repeating
decimal.
1. 3/11
2. -7 3/5
Answer:
1. 0.27 (with bar notation)
2. -7.6
Step-by-step explanation:
What represents a linear function?.
The graph of a straight line represents a linear function.
What is a linear function?Any function with one or two variables and no exponents is said to be linear.
The graph of a linear function is a straight line.
Therefore, the graph of a straight line represents a linear function.
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The owner of a small store buys coats for $45. 00 each. Answer parts a and b. A. He sells the coats for $63. 00 each. What percent of the purchase price is the sale price? The sale price is nothing% of the purchase price
The percentage of the purchase price of the sales price is 55.6%
Given:
The owner of a small store buys coats for $45. 00 each.
He sells the coats for $63. 00 each. What percent of the purchase price is the sale price = ?
Profit = selling price - cost price
Profit = 90-50 = $40
percent of the purchase price is the selling price will be
Purchase or cost price/selling price × 100
= 50/90 ×100 = 55.56%
hence we get the percentage as 55.56%
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HELPPP 60 pointssssss MATH
Answer:
-8
Step-by-step explanation:
y=mx+c
m=y2-y1/x2-x1
-8-0/-7-+1
-8/-8
m=1. c=-1
y=1x+-1
y=x-1
since f(-7)
y=-7-1
y=-8
