As we can assume the relationship is directly proportional, we have to build the proportion and do the cross product. So:
[tex]\begin{gathered} \frac{12cm}{\text{2 nights}}=\frac{18cm}{x\text{ nights}} \\ 12x=2\cdot18 \\ 12x=36 \\ x=\frac{36}{12} \\ x=3 \end{gathered}[/tex]She needs 3 nights
the square practice x² + 6x + 9 = 0
x = -3 twice
Explanation:x² + 6x + 9 = 0
Since the method for solving the question isn't specified, we will be using factorisation method to solve for x.
factors of 9 = 1, 3, 9
The two numbers when multiplied gives 9 and when added gives 6 are +3 and + 3.
using factorisation method:
x² + 3x + 3x + 9 = 0
x(x + 3) + 3(x + 3) = 0
(x + 3)(x + 3) = 0
(x+3) = 0 or (x+3) = 0
x = -3 or x = -3
x = -3 twice
The second method is because of the square practice in the question.
Using complete the square:
x² + 6x + 9 = 0
x² + 6x = -9
we half the coefficient of x and the square the result
coefficient of x = 6
1/2 of coefficient of x = 6/2
square of the result = (6/2)² = 3² = 9
Add the above result from both sides of the equation:
x² + 6x + 9 = -9 + 9
(x + 3)² = 0
square root both sides:
x + 3 = +/- √0
subtract 3 from both sides:
x +3 -3 = -3 +/-√0
x = -3 + 0 or -3 - 0
x = -3 twice
Jimmy wants to make a pentagonal push pop that is 3.25 inches long with a side length of 0.75 inches. Find the surface area of the push pop.
We are asked to determine the surface area of the figure. To do taht we will add the areas of each of the surfaces of the figure. Since it is a pentagon, we will determine the lateral area of one of the surfaces and multiply the result by 5:
[tex]A_l=5sl[/tex]Where "s" is the side length and "l" is the longitude. Replacing the values:
[tex]A_l=5(0.75in)(3.25in)[/tex]Solving the operations:
[tex]A_l=12.19in^2[/tex]What is the best estimate for this sum 1/8+1/6=The sum will be close to?
The expression given is
[tex]\frac{1}{8}+\frac{1}{6}[/tex]The sum of the expression will be,
[tex]\frac{1}{8}+\frac{1}{6}=\frac{6+8}{48}=\frac{14}{48}=\frac{7}{24}[/tex]The sum will be
[tex]\frac{7}{24}[/tex]can someone please help me with question 3 and question 5-7
Question 5
The coordinate of C is (4,4)
If you dilate ABCD by a scale factor of 1/2, the coordinate of the image of C will be:
[tex]\begin{gathered} C^{\prime}(4\times\frac{1}{2},4\times\frac{1}{2}) \\ =(2,2) \end{gathered}[/tex]Question 6
The coordinate of A is (0,2)
If you dilate ABC by a scale factor of 2, the coordinate of the image of A will be:
[tex]\begin{gathered} A^{\prime}0\times2,2\times2) \\ =(0,4) \end{gathered}[/tex]At a fundraiser , a sorority is able to raise $5 less than four times the amount of money a fraternity raises
All together they raised $115
First question what is known is the situation?
Second question what is unknown in the situation
Third question how do I write an equation that represents the situation use at to represent the fraternity
NEED HELP ASAP I WILL MARK YOU BRAINLIEST NO LINKS PLEASE AND THANK YOU
An equation that represents the situation used to represent the amount that the fraternity raises is; x + (4x - 5) = 115
How to solve Algebra Word Problems?Let the amount of money raised by the fraternity be x.
Now, we are told that the sorority raises $5 less than four times the amount that a fraternity raises. Thus;
Amount raised by Sorority = $(4x - 5)
Together, we are told that they raised $115. Thus, the equation will be;
x + (4x - 5) = 115
5x - 5 = 115
5x = 115 + 5
5x = 120
x = 120/5
x = $24
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Answers : • center c and scale factor 2• center a and scale factor 5• center c and scale factor 1• center a and scale factor 2
In order to find the scale factor of the dilation of ΔABC, we just need to divide any pair of the corresponding sides of both triangles. We have that the division of the corresponding sides will be always the same:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{A^{\prime}B^{\prime}}{AB}=\text{scale factor}[/tex]We are going to choose the first division:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor}[/tex]Finding the scale factorWe have that AC = 5 and A'C' = 10:
Then:
[tex]\begin{gathered} \frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor} \\ \downarrow \\ \frac{10}{5}=2 \end{gathered}[/tex]The scale factor is 2.
And since the point C and C' are the same, the center is C.
Answer- A. center C and scale factor 2
solve for x perimeter of the rectangle is 100to x - 8 + x + 4 + 2x - 8 + x + 4 = 100 solve for x
The perimeter of rectangle is 100.
The formula for the perimeter of rectangle is
[tex]P=2(l+w)[/tex]The length of the rectangle is 2x-8 and width of the rectangle is x+4.
The perimeter is
[tex]100=2(2x-8+x+4)[/tex][tex]50=3x-4[/tex][tex]3x=54[/tex][tex]x=18[/tex]Hence the value of x is 18.
The length is
[tex]2\times18-8=36-8=28[/tex]The width is
[tex]18+4=22[/tex]The correct options are 22 and 28.
Triangle a is reflected in the x-axis to give triangle b traingle b is reflected in the y-axis to give triangle a describe fully the transformation that maps a onto c
Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
Is a reflection over the x-axis positive or negative?Thus, we get the conclusion that when a point is mirrored along the x-axis, the x-coordinate stays constant while the y-coordinate deviates from zero. So, M' is the image of the point M (h, k) (h, -k). Guidelines for determining a point's x-axis reflection: I Maintain the x-coordinate, or abscissa.
Thus, the reflection in the x-xis:
The entire x-component is unaltered.
The sign of each y-component is changed from - to + and vice versa.
then, the reflection in the y-xis:
The entire y-component is unaltered.
Every x-component has its sign altered from - to + and vice versa.
Triangle A is transformed into triangle C, and all of the vertices' signs are modified.
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Write an equation in slope intercept form for the line that has a slope of 4/5 and passes through (0,7) Mark only one ovalY=7xY=7x-4/5Y=4/5x+7Y=-4/5x+7
Given:
The slope of the line is
[tex]m=\frac{4}{5}[/tex]Passes through the point
[tex](x,y)=(0,7)[/tex]Required:
To find equation in slope intercept form.
Explanation:
The general equation of slope intercept form is
[tex]y=mx+b[/tex]Where, m = slope
b = y-intercept.
Now,
[tex]y=\frac{4}{5}x+b[/tex]Here The line passes through the point (0,7), therefore the y-intercept is 7.
So,
[tex]y=\frac{4}{5}x+7[/tex]Final Answer:
[tex]y=\frac{4}{5}x+7[/tex]Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm. For a random sample of 134 adult males, the mean pulse rate is 70.1 bpm and the standard deviation is 10.9 bpm. Complete parts (a) and (b) below.
Part A. Express the original claim in symbolic form.
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.9 bpm.
Therefore, the original claim in symbolic form is:
ANSWER:
[tex]\mu=68.9\text{ bpm}[/tex]Part B. Identify the null and alternative hypotheses.
[tex]\begin{gathered} H_0\colon\text{ }\mu=68.9\text{ bpm} \\ H_1\colon\mu\ne68.9\text{ bpm} \end{gathered}[/tex][tex]\begin{gathered} H_0\text{ or the null hypothesis will be based to our claim. We will test if the mean pulse} \\ \text{rate of an adult male is equal to 68.9 bpm.} \\ H_1\text{ or the alternative hypothesis is the one that contradicts the null hypothesis. That is } \\ \text{why our H}_a\text{ has the sign of not equal to (}\ne). \end{gathered}[/tex]
over the last 3 evenings 85 phone calls were received. the second evening she received 5 fewer calls than the first evening.The third evening she received 4 times as many calls how many did she receive each evening
a =20, b =15, c= 60
1) Writing this we have
1st evening: a
2nd evening: b
3rd evening: c
a +b+ c = 85
b=5 -a
c=4a
2) So rewriting this out as an expression we have:
a + b+ c = 85 Plug into that in terms of "a"
a + 5-a + 4a = 85 Combine like terms
4a +5 = 85 subtract 5 from both sides
4a = 80 Divide both sides by 4
a = 20
2.2) Plug into each formula:
b =a -5
b = 20 -5
b = 15
20+15 + c = 85 Add them up
35 +c = 85 Subtract 35 from both sides
c = 85 -35
c= 60
Or we could have done it:
c = 4b
c= 4* 15
c= 60
3) Hence, the answer is a =20, b =15, c= 60
Points A,B,C are collinear. explain what iswrong with this picture. Use the linear pairtheorem in your explanation
SOLUTION
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
For instance
Consider the image given
The measure of the angles are
[tex]\begin{gathered} 129^0and41^0 \\ \text{Hence } \\ A=129^0 \\ B=41^0 \end{gathered}[/tex]The sum of the angles is
[tex]\begin{gathered} 129^0+41^0=170^0 \\ \text{Hence the angles are not linear pair since the summation is not 180 degr}ees\text{ } \end{gathered}[/tex]From the image,
we can see that the angles are not linear pair and hence did not follow the linear pair thorem
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find out
the time at which the rocket will reach its max, to the nearest 100th of a second.
y = -16x² + 217x +96
The time at which the rocket will be at its maximum height, to the nearest 100th of a second is 14 seconds.
Define the term quadratic equation?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2.For the given value of launch of rocket.
Height of the rocket is y in feet.
Time after launch is x in seconds.
The quadratic equation of height is-
y = -16x² + 217x +96
For the maximum height,
Put y = 0.
0 = -16x² + 217x +96
The standard form of quadratic equation is-
ax² + bx + c = 0
On comparing.
a = -16
b = 217
c = 96
Solve equation by quadratic formula and find the roots,
x1 = 217 + √53233 / 32
x2 = 217 - √53233 / 32
Solve both-
x1 = 13.99 = 14 sec
x2 = -0.41 (neglecting negative value)
Thus, the time at which the rocket will reach its maximum height, to the nearest 100th of a second is 14 seconds.
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Write an equation for the line who passes through (-3,1) and (1,3)
Given:
Two points are given as (-3,1) and (1,3)
[tex]\begin{gathered} (x_1,y_1)=\left(-3,1\right) \\ (x_2,y_2)=\left(1,3\right) \end{gathered}[/tex]Required:
We want to write an equation which passes through the given points
Explanation:
First we need to find the slope of the required line
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-(-3)}=\frac{2}{4}=\frac{1}{2}[/tex]The equation of is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{x}{2}+\frac{3}{2} \\ \\ y=\frac{x}{2}+\frac{5}{2} \end{gathered}[/tex]Final answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]Answer:
Step-by-step explanation:
y= r/2 + 3/4
28 ft 20 it 18 ft Given x < 20, which COULD be the area of this trapezoid? 424 ft2 B) 460 +2 464 ft2 5042
Trapezoid area =(Base 1 + Base 2 )Height/2
If x= 20
then area = (28+18)/2 • √ ( 20^2 - 5^2)
. = 23 • √375
. = 445
If x< 20 ,area is
Answer is OPTION A ) 424 ft2
Use the Pythagorean Theorem to find the missi romanille 1 1 point a = 3 and b = 7. Round to two decimal places. Type your answer... 2. 1 point a = 3 and c = 23. Round to two decimal places. Type your answerExercise number 1
The formula of the Pythagorean Theorem is
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} a=3 \\ b=7 \\ c=\text{?} \\ a^2+b^2=c^2 \\ \text{ Replacing} \\ (3)^2+(7)^2=c^2 \\ 9+49=c^2 \\ 58=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{58}=\sqrt[]{c^2} \\ 7.62=c \end{gathered}[/tex]Therefore, the missing side measurement is 7.62 units.
If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar.
If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (7) as the fraction bar
the slope is
m=(17-24)/(15-25)
m=-7/-10
m=7/10
answer is slope is 7/10Jay Field's bank granted him a single-payment loan of $6,800. He agreed to repay the loan in 91 days at an ordinary interest rate of 4.25 percent. What is the maturity value of the loan?
Answer:
$6,872.05
Explanation:
The maturity value of the loan can be calculated as:
[tex]V=P(1+r\cdot t_{})[/tex]Where P is the initial amount, r is the interest rate as a decimal and t is the time in years.
4.25% is equivalent to: 4.25/100 = 0.0425
91 days are equivalent to 91/365 = 0.25 years
Then, the maturity value is equal to:
[tex]\begin{gathered} V=6800(1+0.0425\cdot0.25) \\ V=6800(1+0.011) \\ V=6800(1.011) \\ V=\text{ \$6,872.05} \end{gathered}[/tex]So, the maturity value of the loan is $6,872.05
Evaluate the expression when c = -3/10 and x = -7/8c + 1/5xWrite your answer in simplest form.
Explanation:
if c = -3/10 and x = -7/8
by replacing them in the equation c + 1/5 * x, we get:
[tex]\frac{-3}{10}+\frac{1}{5}*\frac{-7}{8}\text{ = }\frac{-3}{10}-\frac{7}{40}=\frac{-3*4}{10\text{ * 4}}-\frac{7}{40}=\text{ }\frac{-12-7}{40}\text{ = }\frac{-19}{40}[/tex]A 9-meter roll of blue ribbon costs $9.63. What is the unit price?
whats the unit price
can someone please help me find the answer to the following?
Using the Euler formula, we have:
F + V = E + 2 (F: faces, E:edges, V:vertices)
F + 12 = 18 + 2 (Replacing)
F + 12 = 20 (Adding)
F= 8 (Subtracting 12 from both sides of the equation)
The answer is 8.
Answer:
Step-by-step explanation:
1. This polyhedron has 8 faces.
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Find the least-squares regression line y = bo + b₁x through the points
(-2,0), (0,7), (4, 15), (8, 18), (9,24),
and then use it to find point estimates y corresponding to x = 1 and x = 8.
For this problem and to give you practice for the test, use the shortcut method to find bo given that b₁ = 1.9051724137931.
For x = 1, y =
For x = 8, y^=
The values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
Given that, [tex]y = b_{0}+ b_{1}x[/tex]
x y xy xx yy
-2 0 0 4 0
0 7 0 0 49
4 15 60 16 225
8 18 144 64 324
9 24 216 81 576
19 64 420 165 1174 - Total(T)
n = 5
Given line is [tex]y = b_{0}+ b_{1}x[/tex]
Solve for the value of [tex]b_{0}[/tex]
[tex]b_{0} = \frac{Ty*Txx-Tx*Txy}{nTx^{2} -(Tx)^{2} }[/tex]
[tex]= \frac{64*165-19*420}{5*165-(19)^{2} }\\ \\= \frac{10560-7980}{825-361}\\ \\= \frac{2580}{64} = 40.135[/tex]
Solve for the value of [tex]b_{1}[/tex]
[tex]b_{1} = \frac{nTxy-Tx*Ty}{nTx^{2} -(Tx)^{2} }\\ \\= \frac{5*420-19*64}{5*165 - (19)^{2} }\\ \\= \frac{2100-1216}{464}\\ \\= \frac{884}{464} = 1.905[/tex]
Therefore, y = 40.135 + 1.905x
To solve for x = 1
y = 40.135 + 1.905(1)
= 38.23
To solve for x = 8
y^ = 40.135 + 1.905(8)
= 55.375
Hence the answer is the values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
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Find the probability of having 2, 3, or 4successes in five trials of a binomialexperiment in which the probability ofsuccess is 40%.p=[?]%Round to the nearest tenth of a percent.
The probability of having 2, 3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40% is 0.6528.
We are given that:
The probability of the success is = 40%
P(S) = 0.40
Let the random variable be X :
Number of trials = 5 trials
X ≈ B(5, 0.40).
Now, we need to find the probability of having 2, 3, or 4successes in these five trials:
P(2 , 3 or 4 successes in five trials )
= P(X = 2) + P(X = 3) + P(X = 4)
= 0.3465 + 0.2304 + 0.0768
Adding the values:
= 0.6528.
Therefore, the probability of having 2, 3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40% is 0.6528.
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Use the accompanying Venn Diagram, which shows the cardinality of each region,to answer the question below.How many elements belong to set B?
4 elements
Explanation
to find the number of elements that belong to set B, just count the elements inside the circle B
4 elements (3,5,2,9)
I hope this helps you
A box contains letters, shown as MARCHING. What is the probability of the outcome in that order if letters are drawn one by one (a) with replacement? (b) without replacement?
There are 8 letters in the word MARCHING.
So, the number of letters in the box, N=8
b)
The probabilty of drawing the first letter M is,
[tex]P(M)=\frac{1}{N}=\frac{1}{8}[/tex]If the letter is not replaced, the number of remaining letters in the box is 7.
So, the probabilty of drawing the second letter A is,
[tex]P(A)=\frac{1}{7}[/tex]Similarly, the probabilities of drawing letters R,C,H,I, N and G respectively is,
[tex]\begin{gathered} P(R)=\frac{1}{6} \\ P(C)=\frac{1}{5} \\ P(H)=\frac{1}{4} \\ P(I)=\frac{1}{3} \\ P(N)=\frac{1}{2} \\ P(G)=1 \end{gathered}[/tex]So, the probability of of the outcome in that order if letters are drawn one by one without replacement is,
[tex]undefined[/tex]can you help me on the Rolling a 7 part
Rolling a 7
Total outcomes=6*6=36
favorable outcomes
1-6
2-5
3-4
4-3
5-2
6-1
tota favorable outcomes=6
so
The probability of rolling a 7 is equal to
P=6/36
simplify
P=1/6Please Help!!!!! I will give brainliest and 5 stars!!!!
1. A system of linear functions cannot have only two or three solutions, the possible amounts are: Zero, One and Infinity.
2. This is not true because if the lines do not cross, the system has no solutions.
3. Substitution: Explicit variable, such as:
x = 3, y + 3x = 10.y = 2x + 4, 3x + 2y = 20.Elimination: Non-explicit variable, such as:
x + y = 2, 2x + 3y = 5.x - y = 10, 2x + 5y = 40.What are linear functions?Linear functions have the definition given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.A system of linear equations is composed by multiple equations, and the number of solutions is defined as follows:
Zero solutions: slopes are multiples and intercepts are not -> the functions do not intersect on the graph.One solution: different slope and intercepts -> the functions intersect once on the graph.Infinitely many solutions: slopes and intercepts are multiples, hence the functions are the same on the graph.There are two ways to solve the systems, given as follows:
Substitution: one of the variables has an explicit definition.Elimination: none of the variables has an explicit definition.More can be learned about linear functions at https://brainly.com/question/24808124
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I’m trying to figure out how to do this one ! It’s kind of got me stuck
ANSWER :
The answer is Option 3.
EXPLANATION :
From the problem, we have the equation of the line :
[tex]y=x+3[/tex]First thing to do is check the correctness of the table.
The given values in the table must satisfy the equation.
For Option 1.
Let's check the point (2, 3)
[tex]\begin{gathered} y=x+3 \\ 3=2+3 \\ 3=5 \\ \text{ False!} \end{gathered}[/tex]For Option 2.
Let's check the point (-2, 1)
[tex]\begin{gathered} y=x+3 \\ 1=-2+3 \\ 1=1 \\ \text{ True!} \end{gathered}[/tex]But the point (-2, 1) is not in the graph, so this is false!
For Option 3.
The points are the same with Option 2, so we need to check the graph.
(-2, 1) is on the graph.
(-1, 2) is on the graph.
(0, 3) is on the graph.
(1, 4) is on the graph.
(2, 5) is on the graph.
So this must be the correct table and graph.
A 30-m-wide field is how many yard wide?The field is ____ yard wide.( Type a whole number or decimal. Round to three decimal places as needed.)
Given:
30 meter wide field
To determine the field in yards, we convert the given 30 meters into yards.
We must remember that:
1 meter = 1.0936 yards
So,
Therefore, the answer is 32.808 yards.
how to solve the volume of sphere and the area of a cylinder.
Consider a sphere of radius r, then the volume of the sphere is given by,
[tex]V=\frac{4}{3}\pi\times r^3[/tex]Here
[tex]\pi=3.14[/tex]Now let us consider a cylinder of with base radius r and height h, as in the figure,
The area is the total area of the base surface and the niddle surface.
This can be written as,
[tex]A=2\pi(h+r)[/tex]Consider a sphere of radius 2 cm, the volume can be calculated as,
[tex]v=\frac{4}{3}\times3.14\times2^3=\frac{4}{3}\times3.14\times2\times2\times2=33.49cm^3[/tex]