Answer: 7x-5
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(7x+1-8)-(-2)=\boxed{7x-5}[/tex]
Answer:
D. (f-g)(x) = |7x+1|-6
Step-by-step explanation:
f(x) = |7x + 1| - 8
g(x) = -2
(f - g)(x) = f(x) - g(x) = |7x + 1| - 8 - (-2)
(f-g)(x) = |7x + 1| - 6
The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches.
For a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?
For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches.
[tex]P(X < 340) = P(z < \dfrac{(340-320)}{20})[/tex]
= P(z < 1)
= 0.8413
Hence, For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.
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Helppppppp pleaseeeee
Answer:
is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?
calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5
Answer:
13, -2
Step-by-step explanation:
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
When casting the first young Cosette, the casting director has _[blank 1]_ girls to choose from. When casting the second young Cosette, she has _[blank 2]_ girls to choose from, and when casting the third young Cosette, she has _[blank 3]_ girls to choose from.
Match each numbered blank to the answer that correctly satisfies the corresponding blank in the previous sentences.
The required blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.
Theatre company must cast 3 girls.
And has 25 resumes girls who wish audition.
permutation can be defined as study of combinations.
In the question we are asked to calculate the number of girls left after the director chooses.
At first director chooses 3 from 25.
At second director chooses 3 from 22.
At third director chooses 3 from 19.
Thus, the required blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.
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Simplify
b^10/b^2
OA. b^-8
OB. b^5
O c. b^-5
O D. b^8
Step-by-step explanation:
The answer is D)
b^10/b^2
= b^10-b^2 = b^8
hope this helps.pls like and follow if you understand.
thanks:-):-)
The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
The constant of proportionality is given as [tex]k=\frac{y}{x}[/tex] .
Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].
Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:
[tex]k=\frac{4}{2}=2[/tex] .
Therefore, the constant is equal to 2.
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x=5-2y
y-2x=7
A 7-2x
B. 4x-5
C. 5-4x/2
D. 2x + 7
C
when doing substitution,you must make one a subject,which is y in this case.To make y the subject,you must move -2y to 4x to make the y positive,that leaves us with 2y+4x=5.Now move the 4x to 5 to make 2y=5-4x.Lastly,to make y the subject,divide both side by 2 to remove the 2 from the y, which leaves us with y=5-4x/2
40. Noor is packing chocolates into boxes. The boxes come in small, medium and large sizes. A large box holds twice as many chocolates as a medium box and three times as many chocolates as a small box. Noor fills three times as many small boxes as medium boxes and twice as many medium boxes as large boxes. Altogether she packs 1296 chocolates. In total, how many chocolates does she pack into the small boxes.
The number of chocolate which goes into the small boxes is 100 chocolate
EquationChocolate in small boxes = xChocolate in medium boxes = 3xChocolate in large boxes = 3x + 2(3x)= 3x + 6x
= 9x
Total chocolate = 1296x + 3x + 9x = 1296
13x = 1296
x = 1296/13
x = 99.6923076923076
Approximately,
x = 100 boxes
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How many different strings can be made by shuffling the letters in DISCRETEMATHS?
Answer:
I found 14 but their might be more!
hope that helps! :)
Step-by-step explanation:
In AUVW, m/U = (9x - 8)°, m/V = (2x + 2)°, and m/W = (3x + 4)º.
Find m/V.
Answer:
m∠V = 28°
Step-by-step explanation:
In ΔUVW:
m∠U = (9x - 8)°m∠V = (2x + 2)°m∠W = (3x + 4)°To find the measure of angle V, first find the value of x.
Interior angles of a triangle sum to 180°.
⇒ m∠U + m∠V + m∠W = 180°
⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180
⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180
⇒ 14x - 2 = 180
⇒ 14x = 182
⇒ x = 13
Substitute the found value of x into the expression for angle V:
⇒ m∠V = 2(13) + 2
⇒ m∠V = 26 + 2
⇒ m∠V = 28°
Therefore, the measure of angle V is 28°.
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. ?C(lnx+y)dx−x2dy where C is the rectangle with vertices (1, 1), (3, 1), (1, 4), and (3, 4)
By Green's theorem,
[tex]\displaystyle \int_C P(x,y)\,dx + Q(x,y)\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \, dA[/tex]
where [tex]D[/tex] is the interior of [tex]C[/tex]. It's easy to see that
[tex]D = \left\{(x,y) ~:~ 1 \le x \le 3 \text{ and } 1 \le y \le 4\right\}[/tex]
Now,
[tex]\dfrac{\partial Q}{\partial x} = \dfrac{\partial}{\partial x}(-x^2) = -2x[/tex]
[tex]\dfrac{\partial P}{\partial y} = \dfrac{\partial}{\partial y}(\ln(x) + y) = 1[/tex]
so that the line integral reduces to
[tex]\displaystyle \int_C (\ln(x)+y)\,dx - x^2\,dy = -\int_1^3 \int_1^4 (2x+1) \, dy\,dx = \boxed{-30}[/tex]
The function f(x) is graphed. It represents a translation of the square root function g(x) = .
What equation represents the graph of f(x)?
f(x) =
f(x) =
f(x) = – 1
f(x) = + 1
The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
How to determine the equation of f(x)?The complete question is in the attached image
The parent square root function is:
[tex]g(x) = \sqrt x[/tex]
From the graph,
g(x) is shifted one unit right to get f(x)
This is represented as:
f(x) = g(x - 1)
So, we have:
[tex]f(x) = \sqrt {x - 1[/tex]
Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
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1000 mL of D5W is infusing at 20 gtt/min (20 macrogtt/min). Drop factor: 10 gtt/m L.
How long will it take for the IV to infuse? (Express time in hours and minutes
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the drop factor is 10 gtt/mL, hence:
Infuse rate = 20 gtt/min ÷ 10 gtt/mL = 2 mL/min
Time taken = 1000 mL / 2 mL per min = 500 min = 8 hours, 20 minutes.
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
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Answer:
Step-by-step explanation:
900mL of RL is infusing at 80 gtt/min (80 macrodrops/min). Drop factor: 15 gtt/mL
DUE IN 3MINUTes
There is a strong positive linear correlation between rainfall and the number
of peaches a tree produces. Does this mean that more rainfall causes peach
trees to produce more fruit?
A. No. Any number of factors could also be affecting the number of
peaches produced.
B. No. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce less
fruit.
C. Yes. Since rainfall and number of peaches are positively
correlated, this means that more rainfall causes peach trees to
produce more fruit.
D. Yes. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce more
fruit.
Answer:
A. No.
Step-by-step explanation:
The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.
An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.
Bag A contains 7 blue discs, 4 red discs and 1 yellow disc.
Bag B contains 3 blue discs and 6 red discs.
A disc is drawn at random from Bag A and placed in Bag B.
A disc is then drawn at random from Bag B.
Find the probability that the disc drawn from Bag B is red.
Answer:
75% or 65%
Step-by-step explanation: that's what I did at lest
Predict what will happen to the coordinates of a point (x, y) as the point translates to produce point (x′, y′). Assume that the point translates a units to the left or right and b units up or down. Express your answers in terms of x, y, a, and b. Be sure to watch your signs.
Answer:
(x' , y') = ( (x ± 1) , (y ± b) )
Step-by-step explanation:
(object vector) = (x', y')
(translation vector) = ( ±1 , ±b ) ==> Since horizontal movement (x) is right/ or left meaning ±1 , and vertical movement(y) is up or down meaning ±b
Notice that : (image vector) = (object vector) + (translation vector)
therefore (x' , y') = ( (x ± 1) , (y ± b) )
1. What are opposites?
a) Give an example of opposites.
b) Describe a real world situation using opposites.
please make it simple
Answer:A person or thing that is different from other people or things.
Like me and you we might like different things like I like playing games you dont your the opposite of me.
A real world situation would be looking at maybe plants see how different they look or if they look the same study them and realize one is poison the other is fresh.
Step-by-step explanation:
The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
The circumference equal to 25 units
What is perimeter of square?The perimeter of square is 4 times the side.
P= 4* side
The perimeter of the square,
4x = P
Now P is = 32 units then,
32 units = 4(x)
x = 8 inches
So, the diameter of the cylinder formed by the rotation of 8 inches
Now, the circumference of the base is
C = 2πr = πD
If r =8 inches
C = π(8 units) = 8π units
C = 8(3.14) = 25.12 units
Hence, the circumference equal to 25 units
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The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
AMC is a right angle is given. BMD is a right angle is also given. Since XAMC is a right angle, BMC and XCMD are
complementary. Since BMD is a right angle, AMB and BMC are complementary. By the Congruent Complements Theorem,
AMB CMD.
The part of the proof regarding the triangle that is incorrect is By the Congruent Complements Theorem AMB CMD.
How to illustrate the information?From the information given, it should be noted that AMC is a right angle and also that BMD is a right angle.
Therefore, it illustrates that AMC and BMD are equal.
Therefore, by the Congruent Complements Theorem AMC and BMD are equal.
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Which graph represents the relationship?
In the following questions, look at different ways to represent the relation given by the
equation y = x2 - 1.
The table below shows some values for the given equation. Find the values of a and b.
a =
b =
A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, b, 1. The second column is labeled y with entries a, 0, negative 1, 0.
From the values in the table, we can say that the first graph is the correct one that shows some values for the given equation.
How to draw the graph of quadratic functions?We are given the quadratic equation as;
y = x² - 1
From the given table;
At x = -2, y = (-2)² - 1 = 3
At x = -1, y = 0
At x = 0, y = -1
At x = 1, y = 0
Now, from the values above, we can say that the first graph is the correct one that shows some values for the given equation.
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A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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Use
f(x) = 2x − 3
and
g(x) = 4 − x2
to evaluate the expression.
The equation based on the information given will be x⁴ + 8x² - 12.
How to compute the value?It should be noted that from the information given, the expression to compute will be:
= g - g(x)²
This will be:
= 4 - (4 - x²)²
= 4 - (4 - x)(4 - x)
= 4 - (15 - 8x² + x⁴)
= x⁴ + 8x² - 12
The complete question is:
Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².
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PLEASE ANSWER ,in terms of the trigonometric ratios for BCD,what is the lenght of BD? insert text on the triangle in geogebrea to show the lenght of BD. take a screenshot of the triangle with the text,save it,and insert the image in the space below
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
How to calculate the length of BD?In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.
Mathematically, the law of sine is given by this mathematical expression:
sin(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the parameters into the formula, we have;
sin(θ) = BD/BC
sin(74) = BD/9.41
Cross-multiplying, we have:
BD = 9.41 × sin(74)
BD = 9.41 × 0.9613
BD = 9.05 cm.
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
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About 145 out of 500 students prefer walking instead of
riding the bus to school. About what percent of the
students prefer walking?
30%
50%
70%
145%
Answer:
30%
Step-by-step explanation:
[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%
1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
(2) a) Calculate the length of AB.
(2) b) Calculate the slope of AB.
(2) c) Calculate the coordinates of the midpoint of AB.
(2) 2. Determine the radius of the circle .
State the answer as an exact number, and as a decimal rounded to 1 decimal place.
(2) 3 Write the equation of a circle with centre (0, 0) that passes through the point (5, –3)
The length of the line AB as described by points A and B in the task content is; √125.
What is the length of the line?a) The length of AB as described is;
AB = √((7-2)² + (4-(-6))²)
AB = √(25 + 100) = √125.
b) The slope of AB is;
Slope, m = (7-2)/(4-(-6)) = 5/10
Slope = 1/2.
c). The coordinates of the midpoint of AB are;
x = (4+(-6))/2 = -1
y = (7+2)/2 = 4.5
The midpoint is; (-1, 4.5).
2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;
Radius = √((5-0)² + (-3-0)²)
Radius = √(25+9) = √34 = 5.8
3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;
(x-5)² + (x-3)² = 5.8².
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2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3
3.
A = pi x r^2
48 = 3.141... x r^2
÷ by value of pi
15.278... = r^2
Square root the ans, to get r
Thus, R = 3.908..... So, radius is 3.9
2.
Circumference = pi x diameter
87. = 3.141... x d
÷ by value of pi
27.692............. = diameter
Radius is twice the diameter. So, divide diameter by 2 to find the radius.
27.692.....÷ 2 = 13.846...
Thus, radius is 13.8cm
Hope this helps!
8 of 8
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the circular vase is 6.37 * 10^-3 m.
What is pressure?The term pressure is defined as the ratio of force to area. Hence we can write;
P = F/A
F = 15 N
P = 750 N/m2
A = F/P
A = 15 N/750 N/m2
A = 0.02 m^2
Now;
A = πr^2
r = √A/ π
r = √ 0.02/3.142
r = 6.37 * 10^-3 m
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Really need help on this one!!
A
<
Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?
The test value and the p value for the probability are 10.5 and 0.0148.
How to illustrate the probability?Based on the information, the observed and expected values will be:
Observed. Expected
75. 75
100. 120
90. 75
15. 30
The p value based on the test statistic from the distribution table will be 0.0148.
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20 points/ Brainliest!!
What set of transformations are applied to parallelogram ABCD to create A”B”C”D?
Answer:
A) Reflected over the x axis and reflected over the y-axisStep-by-step explanation:
ABCD moves 2 quadrants, so has to move over 2 axes.
So, the only option that would work is A).
Hope this helps.