Step-by-step explanation:
Simplifying 8a = 2xy + b
Reorder the terms: 8a = b + 2xy
Solving 8a = b + 2xy
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Divide each side by '8'. a = 0.125b + 0.25xy
Simplifying a = 0.125b + 0.25xy
A DVD player costs $96.34, with sales tax included. What is the original price of the DVD player if the sales tax rate is 8.25%?
The original price of the DVD player if the sales tax rate is 8.25% is $88.79
Sales taxCost of DVD player including tax = $96.34Sales tax = 8.25%Original cost = 8.25%Total cost = original cost + (sales tax × original cost
96.34 = x + (8.5% × x)
96.34 = x + (0.085 × x)
96.34 = x + 0.085x
96.34 = 1.085x
x = 96.34 / 1.085
x = 88.7926267281105
Approximately,
x = $88.79
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Adding and Subtracting Functions
F(x)=x^2+4
G(x)=x-1
Find (g+f)(x)
Answer:
Step-by-step explanation:
[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]
In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor constructing nuclear plants
The p value for the difference is 0.005.
According to the statement
we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.
And we have to find the difference between them in proportions.
So,
X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
X2 = 70 represent the number of people suburban residents are in favor
N1 = 100 sample 1 selected
N2 = 125 sample 2 selected
AND
P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)
Pv represent the value for the test (variable of interest)
Here we apply the Z test to find the difference then
Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2
Now after solving
Z = 2.795.
Now The significance level provided is ,and we can calculate the p value for this test.
Since is a two tailed test the p value would be:
P = (z>2,795)
P = 0.005.
So, The p value for the difference is 0.005.
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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Find the measure of arc CFD.
The measure of the Central Angle indicated is; 45°
How to find the central angle of a circle?
The central angle will be the angle subtended at the center by arc FE and arc CB.
Now, we see that angle ∠FOB = 135° and since we know that sum of angles on a straight line is 180°, then we can say that;
Central Angle = 180° - 135° = 45°
Angle subtended by Arc CD at the center is;
θ = 180 - (81 + 45)
θ = 54°
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Please help!
Which of these r-values represents the weakest correlation?
A. 0.2
B. 0.3
C. 0.4
D. 0.1
Answer: 0.1
Step-by-step explanation:
The smaller the absolute value of the correlation coefficient, the weaker the correlation.
Please if anyone no math I really need help
Answer:
c
Step-by-step explanation:
option a (x-4) translates the graph 4 units right, not down
option b (x)-4 translates the graph 4 units down, not left
option c (x)+4 translates the graph 4 units up, so it is correct
option d (x+4) translates the graph 4 units left, not right
if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down
if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left
I have no idea how to do this
The solution for the given equation X^3 + Y^2 = 971,028. So, option A is correct.
What are multiples?A multiple of a number is the number whose remainder is 0 when divided by the given number.
Consider 'a' as the multiple of a number 'n'.
Then, a ÷ n = b (and remainder = 0)
Calculation:It is given that,
X = largest 2-digit multiple of 3 which is not a multiple of 5
⇒ X = 99
Y = smallest 2-digit multiple of 9 which is not a multiple of 6
⇒ Y = 27
Then, substituting the values in the given equation,
= X^3 + Y^2
= (99)³ + (27)²
= 970,299 + 729
= 971,028
Therefore, the value of the given equation is 971,028.
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During a very cold winter, water pipes sometimes burst because:
The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.
Bursting of Water Pipes During a Very Cold Winter
The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.
As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.
The pressure that the ice builds up inside the pipes could rupture the pipe walls.
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If c(x) = 4x − 2 and d(x) = x² + 5x, what is (c.d)(x)?
4x³ + 18x² – 10x
x² + 9x-2
16x² + 4x-6
4x² + 20x-2
Answer:
[tex]4x^2+20x-2[/tex]
Step-by-step explanation:
To find (c.g)(x) we basically use the function d(x) as your variable, x, and plug it into c(x). So we replace every x in c(x) with the function d(x), [tex]x^{2} +5x[/tex]
c(g(x))=4(x^{2} +5x)-2
c(g(x))4[tex]x^2[/tex]+20x-2
Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
The side lengths that forms a right triangle are as follows:
11, 13 √2907, 24, 25What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides of the triangle follows Pythagoras theorem.
Therefore,
c² = a² + b²
where
a and b are the legsc is the hypotenuseThe hypotenuse is the longest side of the right triangle.
Therefore, the side lengths that forms a right triangle are as follows:
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Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials
Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.
What is Systemic chemotherapy?Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).
Some Key features of systemic chemotherapy are-
Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.To know more about Chemotherapy, here
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A manufacturer makes ball bearings out of motel steel. it takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter
Using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
According to the question,
It takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter.
Radius = 1/2 = 0.5 cm
volume V of one ball bearing is: V=(4/3)*π*r³
= 4/3 * π * (0.5)³
=0.524 cm³
In order to find number of ball bearings out of molten steel only if we divide the volume of steel by the volume of the ball bearing
5.24/0.524=10.
Hence, using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
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Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.
The central angle formed between the ends of the ribbon is 98.6°.
How to illustrate the angle?The circumference will be:
= πd
= 3.14 × 15 = 47.1
Ribbon = 60 - 47.1 = 12.9
Length of arc = x/360 × πd
12.9 = x/360 × 3.14 × 15
x = 98.6°
The angle is 98.6°
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In the biblical account, adam lived to be how old?
a. 99
b. 122
c. 545
d. 930
Find the perimeter of the rhombus below, given that a = 7 and b = 14. (round your answer to one decimal place, if necessary.)
If the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
Given that the value of a is 7,b is 14.
We are required to find the perimeter of the rhombus.
The values which are given to us are of the lengths of diagonals of rhombus.
Perimeter of the rhombus is equal to 4 times the side of the rhombus. So in order to find the perimeter of the rhombus we need the side of the rhombus not the diagonals.
When we draw the diagonals in the rhombus it forms four right angled triangle in which the Base is equal to 7/2 units and 7 is the perpendicular.
We have to use pythagoras theorem to find the hypotenuse which is the side of the rhombus.
Suppose base is BC , perpendicular is AB and hypotenuse is AC.
AC=[tex]\sqrt{7^{2} +7/2^{2} }[/tex]
=[tex]\sqrt{49+49/4}[/tex]
=[tex]\sqrt{245/4}[/tex]
=7.826
Perimeter of rhombus=4*side
=4*7.826
=31.304
After rounding off it will be 31.3 units.
Hence if the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
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Question 5 of 10
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2
that passes through (-6, -1).
A. y = 5x + 29
B. y = -5x - 11
C. y = x +
OD. y = 5x - 29
SUMIT
Answer:
A
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 5.
[tex]y+1=5(x+6) \\ \\ y+1=5x+30 \\ \\ y=5x+29[/tex]
Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Solving an inequality, we will see that there is less than $280 in the pile of money.
How much money is originally in the pile?Let's say that the amount of money is defined by the variable.
First, we know that Jeri keeps $80, so now in the pile we have:
M - $80.
Now she gives one third of that, then the leftover is:
(2/3)*(M - $80) + $80
We know that this is more than:
M - $200
Then we have the inequality:
(2/3)*(M - $80) + $80 > M - $200
And we can solve this for M.
(2/3)*M - (2/3)*$80 + $80 > M - $200
(1/3)*$80 + $200 > M - (2/3)*M
(1/3)*$80 + (1/3)*$200 > (1/3)*M
$280 > M
Then we conclude that there is less than $280 in the pile of money.
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6. At the local community center, they've decided to build a pool in the
shape of a rectangular prism. The length of the pool is 27 feet and the
depth is 12 feet. Also, the area of the base of the pool must be 864 square
feet. What is the width of the pool?
32 feet
64 feet
13.7 feet
123 feet
Answer:
width = 32 ft
Step-by-step explanation:
Divide the base area (864 ft^2) by the length (27 ft). We don't need to know the depth of the pool to solve this problem.
864 ft^2
------------- = width = 32 ft
27 ft
Kindly solve this please!
Diagram for both the questions are given.
Answer:
Q9 - B) 8Q10 - D) 4.5========================
Question 9We have a diagram and need to find the number of routes without repeat paths:
[tex]ABCA[/tex] or [tex]ACBA[/tex]We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
[tex]ABCA = 1*2*2 = 4[/tex][tex]ACBA = 2*2*1 = 4[/tex]Total number is:
[tex]4 + 4 = 8[/tex]The matching answer choice is B
---------------------------------------------------------------------------
Question 10From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
[tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
[tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]As per ratio of corresponding sides:
[tex]AE/DE = 1/3[/tex]As per segment addition:
[tex]AE + DE = AD = 4[/tex]From the two equations above we get:
[tex]DE = 3/4*AD = 3/4*4 = 3[/tex]Now, the required area is:
[tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]This is matching the answer choice D
Answer:
9) B. 8
10) D. 4.5
Step-by-step explanation:
Question 9
For ease of visualization, label the different legs of the journey on the diagram (see attachment).
The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.
The different routes are:
AB (u), BC (x), CA (w)AB (u), BC (y), CA (w)AB (u), BC (x), CA (z)AB (u), BC (y), CA (z)AC (w), CB (x), BA (u)AC (z), CB (x), BA (u)AC (w), CB (y), BA (u)AC (z), CB (y), BA (u)Therefore, there are 8 different routes.
Question 10
Triangles EDC and EAB are similar since they have congruent angles:
∠EDC ≅ ∠EAB (both right angles)∠DEC ≅ ∠AEB (vertical angle theorem)Therefore, their corresponding sides are in proportion.
⇒ CD : BA = ED : EA
⇒ 9 : 3 = ED : EA
⇒ 3 : 1 = ED : EA
Since we know that AD = 4:
⇒ ED = 3
⇒ EA = 1
Area of a triangle
[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]
To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.
[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]
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What is the area of this triangle?
Answer:
12 units^2
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
base goes from -4 to +4 = 8 units
Height goes from 1 to 4 = 3 units
area = 1/2 * 8 * 3 = 12 units^2
Which term describes the red curve in the figure below?
• A. Hyperbola
B. Circle
C. Parabola
• D. Ellipse
A cone has a circular base. So, the answer to your question is B for circle.
Find the volume of a rectangular prism with the following dimension 2cm by 3cm by 4cm
Answer:
24 cm³
Step-by-step explanation:
V = LWH = 2 × 3 × 4 cm³ = 24 cm³
HELP PLS PLS!!!! look at pic
Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]
Step-by-step explanation:
To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]
Which of the following is a perfect square trinomial?
a. x^2+10x+25
b. x^2+6x+13
c. x^2+100
d. x^2+3x+9
Answer:
a. x² + 10x + 25
Step-by-step explanation:
because
(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25
so, it is a perfect square of (x + 5).
Which rule can be used to describe the growth of the y-values of the function y=12^(x) each interval from x=-1 to x=3
A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
How to determine the rule?By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.
For instance, we have:
At x = -1
y = 12^(-1)
y = 1/12
At x=0
y = 12^(0)
y = 1
At x = 1
y = 12^(1)
y = 12
In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
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10 POINTS
please help me!!
Please help me
The sum of an integer and its square is 210. Find the integer. Include a completer
solution
Answer:
14
Step-by-step explanation:
An integers are whole numbers and their opposites. ...-3,-2,-2,0,1,2,3...
I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).
14 + (14)(14) = 210
Answer:
refer to the attachment
A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.
The y-intercept of the linear function is y = 0.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.
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Identify the relationship between the variable:_____ is a function of __
Ps need asap
A correlation is simply used to determine whether a relationship exists between the variables.
How to illustrate the information?The information is incomplete and an overview will be given. The correlation shows the relationship between the variable.
This can be explained in a numerical form that's known as the correlation coefficient. This shows that strength of the relationship.
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Which statement is true regarding the graphed functions?
I need help and can’t find the answers anywhere
Answer:
f(0)=g(0)
Step-by-step explanation:
The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.