The value of f(7) is 9 given that f(x) = |19 - 4x|
How to determine the value of f(7)?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Given: f(x) = |19 - 4x|
To find f(7), substitute x = 7 into f(x) = |19 - 4x|:
f(7) = |19 - 4(7)| = |19-28| = |-9| = 9
Note: The sign | | means absolute, the sign of any value inside it will be discarded and only the number is written
Therefore, f(7) is 9
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3/8=15/5x-2 please help me find x
Answer x = 19/24
Step-by-step explanation:
The area of a rectangle is 110 square units. It’s length measures 11 units. Find the length of diagonal
The diagonal of the rectangle is 14.87 units.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area of rectangle = 110 square units
Length = 11 units
Area of a rectangle = Length x Wide.
110 square units = Length x Wide
110 = 11 x Wide
Wide = 110/11
Wide = 10
Now,
The diagonal of a rectangle.
Using the Pythagorean theorem we get,
Diagonal² = Wide² + Length²
Diagonal² = 10² + 11²
Diagonal² = 100 + 121
Diagonal² = 221
Diagonal = √221
Diagonal = 14.87 units.
Thus,
The diagonal of the rectangle is 14.87 units.
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a medical researcher is studying the effects of a drug on blood pressure. subjects in the study have their blood pressure taken at the beginning of the study. after being on the medication for 4 weeks, their blood pressure is taken again. the change in blood pressure is recorded and used in doing the hypothesis test.change: final blood pressure - initial blood pressurethe researcher wants to know if there is evidence that the drug reduces blood pressure. at the end of 4 weeks, 35 subjects in the study had an average change in blood pressure of -2.4 with a standard deviation of 5.2.find the p -value for the hypothesis test. your answer should be rounded to 4 decimal places.
Answer: 0.0099
Step-by-step explanation:
15. Mindy has $20. She spent $8.64 including tax to buy a new card game. She
needs to set aside $10 to buy lunch. If Lollipops cost $.28 including tax, what is
the maximum number of lollipops that Maya can buy?
Step-by-step explanation:
she can therefore only spend $10 of the $20.
$8.64 are adjust gone for the card game.
that leaves us with
10 - 8.64 = $1.36
to spend on lollipops.
1 lollipop costs $0.28
so, she can buy a many lollipops as times 0.28 fits into 1.36 :
1.36 / 0.28 = 4.857142857...
that means she can buy 4 lollipops max.
she would keep some change, but not enough to buy a 5th lollipops, because then she would have to cut into the $10 reserve she needs for lunch.
for 5 lollipops she would need $1.40 (5×0.28).
Alexa conduct a scientific experiment. For certain time, The temperature of a compound rose 3 1/2° every 2/3 of an hour. How much does a temperature of the compound rise in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
PLEASE HELP!!!!
Please Help. The depth at which whales dive, y, in feet, as related to the duration of the dive, t, in seconds, is represented by the linear model y hat equals 4.8 plus 11.23 times t. If the dive duration is 5 seconds, what is the predicted depth of the dive?
0.02 feet
60.95 feet
−60.95 feet
−0.02 feet
Using the linear function, the depth of the dive at 5 seconds is 60.95 feet
Linear FunctionLinear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.
In this question, we can represent the problem using a linear function or equation and plug in the value of our unknown.
y = 4.8 + 11.23t
Using this function, we can find the depth at 5 seconds;
y = 4.8 + 11.23(5)
y = 60.95ft
The depth of the whale at 5 seconds is 60.95 feet
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what is the relative frequency of all students surveyed who go to cook middle school and prefer energy flow?
Answer:
2/5 = 0.4 = 40%
Step-by-step explanation:
You want the relative frequency of students who go to Cook Middle School and prefer Energy Flow.
Table valuesThe table tells us the number of students who go to Cook Middle School is 35, of which 20 prefer Energy Flow. The total number of students is 50.
Relative frequencyThe relative frequency of interest is ...
(Cook & Energy Flow) / (All students)
= 20/50 = 2/5 = 0.4 = 40%
The relative frequency of students who go to Cook and prefer Energy Flow is 2/5, or 40%.
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Sathish is going on a 210021002100-kilometer road trip with 222 friends, whom he will pick up 150150150 kilometers after he begins the trip and drop off when there are 150150150 kilometers remaining. the car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter.
Sathish will pay $64.8
When Satish is alone, kilometres:
Beginning at 150 kilometres and ending at 150 kilometres will be travelled 300 kilometres in total
When Satish is with friends, the total kilometres travelled is 2100 km:
And when Satish went alone he travelled 300 km
When Satish is with friends, total kilometres travelled: 2100-300 = 1800 km
Gas consumed in litres when Satish is alone: 100 kilometres use 6 litres of gas.
300 kilometres at 6 x 3 equals 18 litres.
So, when Satish is with friends, litres of gas are consumed: 100 kilometres use 6 litres of gas.
So, 6 × 18 for 1800 kilometres is equal to 108 litres.
Gas prices when Satish is on his own:
$1.2 per litre
18 x $1.2 = $21.6
Gas prices when Satish is travelling with friends
$1.2 per litre
108 x 1.2 = $129.6
Cost for each friend = $129.6/3 = $43.2
Satish will pay: Cost when travelling with friends + Cost when travelling alone
=$43.2+ $21.6
=$64.8
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A 850 kg car is moving with a speed of 10 m/s. Which of the following would cause the largest change in momentum?
a. Double the velocity and mass
b. Double the velocity and cut the mass in half
c. Keep the velocity the same and triple the mass
d. Cut the mass and velocity in half
The largest change in momentum will happen when the velocity and mass of the object are doubled( option A)
What is momentum?The momentum of a body is the product of the mass of the body and it's velocity. Momentum is measured in kg/ms^-1. It is a vector quantity. it is represented by p
Momentum of a body is expressed as p= m× v
where m is the mass of the body and v is it's velocity. This means that the higher the mass and velocity of the body the higher it's momentum.
The initial momentum of the body of mass 850kg and velocity 10ms^-1 = 850kgms^-1
When the velocity and mass are doubled , then the new momentum will be 1700× 20= 34000kgms^-1
Therefore the largest change in momentum will be obtained when both mass and velocity are doubled.
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If B=x^{2}+ 2 and C=2+2x^{2}find an expression that equals 2B+C in standard form.
The expression that equals 2B+C in standard form is 4x² + 6
How to determine the expression?From the question, we have the following parameters that can be used in our computation:
B = x² + 2
C = 2 + 2x²
The expression to calculate is given as
2B + C
Substitute the known values in the above equation, so, we have the following representation
2B + C = 2x² + 4 + 2 + 2x²
Evaluate the like terms
2B + C = 4x² + 6
Hence, the expression is 4x² + 6
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if the same data are analyzed using a one-way anova and the randomized block design, the sums-of-square between groups (ssb) is:
Using One way ANOVA and Randomized block design, the sum of squares between groups (ssb) is equal to the sum of sum of sum of explantary variable A's sum of squares and errors sum of square.
Statistics uses one-way ANOVA to compare the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means. It is constructed using the sum of squares measure of total variability used in the numerator of the standard deviation, subtracting the mean, squaring the difference, and adding all observations to obtain the total variability Generate a scale. For multiple groups, we focus on decomposing this total variability (total sum of squares) into the variability between means (the sum of squares of the explanatory variable A) and the variability of the residuals or errors (the error sum of squares).
SSTotal = sum of squares = ∑( yᵢ - Y )²
Total variation is assessed by the total mean (the estimated mean of all observations, available from mean-only models).
SSA = Sum of Squares of Explanatory Variable A
Also called treatment, regression, or model sum of squares. ∑∑(yᵢⱼ - Y' )²
SSE = error (residual) sum of squares
Variation of response around group mean.
Also called the sum of squared residuals.
SSE = ∑∑( Y - Y')²
The total sum of squares is always equal to the sum of the sum of the squares of the explanatory variable A and the sum of the squared errors, SST (total) = SSA + SSE. This equation means that if SSA increases, SSE must decrease if SSTotal remains the same. This result is called the sum of squares decomposition formula.
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a house is 13 ft tall. its shadow is 20 ft long at the same time the shadow of a nearby building is 170 ft long. find the height of the building.
The height of the building after using proportion is 110.5 ft.
What is proportion ?
The main conceptual underpinnings on which proportion is described are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers. For grasping the myriad concepts in science and mathematics, the ratio and proportion are crucial constructing elements. With the right amount of proportion, a variety of problems in daily life, such as those encountered in the kitchen or in business when processing transactions, can be resolved. It facilitates comparison by establishing a relationship between two or more quantities.
Here House height = 13ft
Shadow of the house height = 20 ft
Shadow of the building height = 170ft
Noe using proportion ,
=> [tex]\frac{House height}{shadow of the house} = \frac{building height}{shadow of the building}[/tex]
=> [tex]\frac{13}{20} = \frac{x}{170}[/tex]
=> x=[tex]\frac{13*170}{20}[/tex] =110.5 ft.
Hence the height of the building is 110.5 ft tall.
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HELPPPP I NEED THIS QUICKLY!!
A) Yes it is a function and f(x)=2.80+3.50x so 2.80 is an independent function and 3.50x is dependent function
B) Domain x = (0,20] and Range y = (2.8,72.8]
A dependent function is what?
A dependent function type is one whose outcome depends on the parameters of the function.
Independent function: What is it?
Independent function (plural independent functions) as a noun (mathematics) any one of a group of functions whose value cannot be inferred from the values of all the others.
Given: The expression y = 3.5x + 2.8 calculates the y (in dollars) cost of an x-mile taxi fare. You have enough cash to take a cab for a maximum of 20 kilometres.
Domain and range to find
Solution:
y = 3.5x + 2.8
cost y (in dollars)
miles, in.
You have enough cash to take a cab for a maximum of 20 kilometres.
0 < x ≤ 20
Therefore, x = [0, 20].
Domain x = [0, 20]
y = 3.5x + 2.8
x = 0
=> y = 0 + 2.8 = 2.8
x = 20
=> y = 3.5(20) + 2.8
=> y = 70 + 2.8
=> y = 72.8
2.8 < y ≤ 72.8
y = (2.8 , 72.8 ]
Range = (2.8 , 72.8 ]
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Find the domain and range of the function f(x)= √9-x² . OR. Let f ...
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Consider this function. f(x) = |x – 4| + 6 If the domain is restricted to
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In this figure, lines L and M are parallel.
What is the measure of angle w?
60\degree60°
100\degree100°
120\degree120°
128\degree128°
Sarah has 21.50 to go grocery shopping. On her way to the store, she donates 3.00 to a canvasser for a charity. IF mangoes cost 2.25 at the store that day, how many mangoes can she purchase if she uses up all of her remaining money
Sarah can purchase 8 mangoes with all her remaining money
How to find the number of mangoes she can purchase using her remaining money?Given that:
Sarah has 21.50 to go grocery shopping
She donates 3.00 to a canvasser for a charity (that is subtraction).
Thus, the remaining money = 21.50 - 3.00 = 18.50
If mangoes cost 2.25. In order to know how many mangoes she can purchase if she uses up all of her remaining money, you have to divide the remaining money (18.50) by the cost of the mangoes (2.25). Thus:
Number mangoes = remaining money /cost of mangoes
Number mangoes = 18.50 / 2.25 = 8
Therefore, she can purchase 8 mangoes if she uses up all of her remaining money
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The garden club at Central Middle School is planting a flower bed. A scale drawing of the flower bed is shown. The scale is 1 in. : 2 ft.
Answer:
16 and 12
Step-by-step explanation:
A.1 IN=2FT
8IN =2(8)FT
= 16
B.1 IN=2FT
6IN=2(6)FT
=12 FT
the number of homes sold by a realtor during a month has the following probability distribution: number sold probability 0 0.20 1 0.40 2 0.40 what is the probability that the realtor sells no more than one house during a month?
The probability that the retailer sells no more than one house in a month is 0.60.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes and how likely they are to happen. The analysis of events governed by probability is called statistics.
The given is a probability distribution. The probability density function or PDF of the probability is defined for the random variable x, where x ranges from 0 less than or equal to x less than or equal to 2 ie the range of x is from 0 to 2 with 0 and 2 inclusive.
x : 0 1 2
p(x): 0.20 0.40 0.40
The probability that the retailer sells no more than one house in a month is given by
P(x less than or equal to one) = P(0) + P(1)
=0.20 + 0.40 = 0.60.
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Write a linear function f with the given values f(0) = 2, f(3) = -1
The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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consider the mad statistic. what would happen if you did not take absolute values before calculating the sum of differences between group means? why would this not be a useful calculation without taking absolute values?
This type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
We are asked that, what would happen if you did not take absolute values before calculating the sum of differences between group means.
As, when we calculate the differences between group means then, some of the values may be negative.
When we add those negative values while evaluating the sum then the sum can be less than the absolute and to get over from this type of problem we always take absolute values of the differences between group means and then get the sum.
Also, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
Hence, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
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Which parabola below has a maximum value?
a. y = 0.1x2 - 3x
b. y = 4x2 + 24x +23
c. y = 2x - 3x2
d. y = x2 + 2x + 20
In the given parabola equations, the third equation [tex]y = 2x - 3x^{2}[/tex] has a maximum value.
What is the Maximum parabola?
If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).
We have,
[tex]y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20[/tex]
For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).
By Simplifying the third equation we get its leading coefficient is negative (a < 0).
[tex]y = -3x^{2} + 2x[/tex]
Hence in the given parabola equations, the third equation has a maximum value.
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it is known that 15% of the calculators shipped from a particular factory are defective. what is the probability that exactly four of ten chosen calculators are defective?
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, whereC5 3= 5!/3/2=4*5/2=10p is the probability that one randomly selected calculator is defective= 10%=0.1q is the probability that one randomly selected calculator is non-defective.q=1-p=1-0.1=0.9So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081learn more about probability click here:
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The length of KL¯¯¯¯¯¯¯¯ is 8x−17 units. The length of ST¯¯¯¯¯¯¯ is −2x+18 units. For what value of x are the segments congruent?
NO LINKS OR FILE
Answer:
x = 3.5units
Step-by-step explanation:
Congruent means the same length, so set the given lengths equal to each other.
8x - 17 = -2x + 18
Add 2x to both sides.
10x -17 = 18
Add 17 to both sides.
10x = 35
Divide by 10
x = 3.5
When x is 3.5, KL and ST are the same length. Check.
8(3.5) - 17 = 11
and
-2(3.5) + 18 = 11
Here is a set of data
2.4, 1.6, 3.2, 0.3, 1.5
Each piece of data is now doubled
Work out the new mean
Answer:
The new mean is 3.6
Step-by-step explanation:
Since each piece of data is now doubled that means the data is now
4.8, 3.2, 6.4, 0.6, 3
Add up all of the data which comes out to 18
Divide 18 by the number of numbers there are which is 5
This will get you 3.6 which is the new mean of the data
consider the following data set which is the time (in minutes) for students to finish a math test. 34 45 27 33 38 41 45 29 30 39 34 40 28 33 36 50 (a) what is the sample mean? (b) what is the sample standard deviation? (c) construct a 99% confidence interval for the population mean.
a) Sample mean of set is 36.375.
b) Standard deviation of sample is 6.66208.
Define mean and standard deviation.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Given,
a) Mean
Total number of values = 16
= Sum/Total number of values
= 34 +45+ 27 +33 +38+ 41+ 45 +29 +30+ 39 +34 +40 +28 +33 +36+ 50/16
= 582/16
= 36.375
Sample mean of set is 36.375.
b) Sample standard deviation
S² = ∈ (x i - x)²/N-1
S² = 666.75/16-1
S² = 44.383333
S = √44.38333
S = 6.66208
Standard deviation of sample is 6.66208.
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out of 150 coins, 90 are quarters. of the remaining coins, 40% are nickels and the rest are dimes and pennies. there are 5 dimes for every penny. how many pennies are there?
There are 6 pennies in a total of 150 coins.
Given that,
Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.
and also,
For every penny, there are five dime.
Total = 150 coins
Out of it, 90 are quarters so the remaining coins are 60
It is said that,
In that 60 coins 40% are nickels which means
40% of 60 is 24
So remaining coins are 36 (by subtracting 24 from 60)
It is said that there are 5 dimes for every penny which means
Using Algebra,
x + 5x = 36
6x= 36
x= 6
Therefore, there are 6 pennies in a total of 150 coins.
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A hiking guide recommends that a person wear snowshoes when the accumulated snow has a depth of at least 6 inches. At 8:00 a.m., the depth of snow in a certain area is 4 inches. The predicted average rates of change of the depth of snow for different time intervals are shown in the table. For which of the following time periods between 8:00 a.m. and 8:00 p.m. would the guide recommend wearing snowshoes?
A. 8:00 a.m.-10:00 a.m. and 1:00 p.m.-3:00 p.m.
B. 8:00 a.m.-11:00 a.m. and 3:00 p.m.-4:00 p.m.
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
D. 9:00 a.m.-11:00 a.m. and 2:00 p.m.-4:00 p.m.
Considering the average rate of change, the time periods in which snowshoes are recommended are given as follows:
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function (change in the numeric value) divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The initial amount is of 4 inches, hence, considering the rates, the amounts of snow on the ground are given as follows:
11 am: 4 + 3 x 0.75 = 6.25 inches. (>6 at 10 am).3 pm: 6.25 - 4 x 0.25 = 5.25 inches.8 pm: 5.25 + 5 x 0.50 = 7.75 inches. (>6 at 5 pm).Hence the intervals are given by option c.
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The function f(x) = (x + 5)(x-3) is dilated by x to produce
the function g(x) = x f(x). How many x-intercepts does
3. the function g(x) have?
Function g(x) have 3 x intercepts.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The function f(x) = (x + 5)(x-3) is dilated by x to produce the function
the function g(x) = x f(x).
A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size
g(x)=x(x + 5)(x-3)
=x(x²-3x+5x-15)
=x(x²+2x-15)
x=0, x=-5 and x=3
The function g(x) have 3 x intercepts.
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The sides of a triangle are in the form of consecutive even integers. If its perimeter is 48cm, find the
measure of each side.
Answer:
The sides of the triangle would be 14, 16, and 18.
Step-by-step explanation:
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May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Select the ordered pair that is NOT marked on the coordinate plane.
An ordered pair that is not marked on the coordinate plane of this graph is (8, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which represent the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), in order to represent the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
By critically observing the given graph, we can reasonably and logically deduce that data point (8, 0) is the missing ordered pair on the coordinate plane.
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Solve the equation x/2 + 1 = 5x
Answer:
9/2
Step-by-step explanation:
X/2+1=5x
(X+2)/2=5x
x+2=10x
2=9x
X=9/2