First answer:
If you look carefully to the measures of the three triangles that are the ramps of the exercise, you will notice they are similar after comparing them.
• Ratio of Ramp 1 = 2/3
,• Ratio of Ramp 2 = 4/6
,• Ratio of Ramp 3 = 6/9
Second answer
The information is given on the image and we can calculate the missing measures for make a smooth slide:
• Ramp 1 - Base 10 - Height 12
,• Ramp 2 - Base 15 - Height 18
,• Ramp 3 - Base 30 - Height 36
We used the ratio 2/3 for answering the first question, now we have the ratio
5/6, as follows:
• Ramp 1 - 5/6 * 2/2 = 10/12
,• Ramp 2 - 5/6 * 3/3 = 15/18
,• Ramp 3 - 5/6 * 6/6 = 30/36
8. James is at a gift sale where everything costs $4 (tax included).James has $50.James must have at least $28 rer ining when he is finished buyinggifts.What is the greatest number of gifts James can buy?
Let the number of gift be x
The total amount James has is $50
Since he must have $28 remaining
Thus, the amount he would spend must not exceed
[tex]\text{ \$50-\$28=\$22}[/tex]Therefore,
If for every gift, $4 tax is included
[tex]x\text{ }\times\text{ \$4 =\$4x}[/tex]The number of gift James can buy
[tex]\begin{gathered} 4x\leq22 \\ x\leq\frac{22}{4} \\ x\leq5.5 \end{gathered}[/tex]Hence, the maximum number of gift James can buy is 5
help meeeeeeeeee pleaseee
Inequalities define the relationship between two non-equal values. Inequality means being unequal.
option C is the correct Graph.
Relation { x | -7 < x < 3} .
solution in interval notation ( -7 , 3 ) .
Why do we study inequalities?To comprehend inequality, one must first comprehend the modern world and the forces that shaped it. More specifically, understanding inequality is a prerequisite for overcoming it: that is, for healing past wounds, generating social solidarity, and rebuilding a more just society.According to experts, inequality stifles economic growth and fosters political dysfunction. Because rich households spend less of their income than poorer households, concentrated income and wealth reduces the level of demand in the economy. Reduced opportunities for low-income households can also have a negative impact on the economy.To learn more about : Inequality,
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which ratio is equivalent to 1 and 8 a.7 to 14b. 7 to 9c.6 to 41d.6 to 48
we can see that
[tex]\frac{6}{48}=\frac{6}{6\cdot8}=\frac{1}{8}[/tex]hence, the answer is d).
Evaluate f(x) at the given values of x.
f(x) = 4x x = -5, 3
Step-by-step explanation:
x=-5 f(x)=4x
f(x)=4(-5)
f(x)=-20
x=3 f(x)=4(3)
f(x)=12
24 lemons are required to make 32 gallons of lemonade. How many lemons are needed to make 4 gallons of lemonade?
Answer:
Step-by-step explanation:
Simple:
24:32
?:4
This means just divide by 8 to get four. This also means to divide 8 for 24 also
24/8:4=
3:4 as answer
find f(6). evaluate the function graphically.
F(6) IS TRYING TO ASK YOU WHAT IS THE VALUE OF Y WHEN X IS EQUAL TO 6 IN THE GRAPH.
VALUE OF Y WHEN X IS EQUAL TO 6 IN THE GRAPH.IF TOU CHECK IN THE GRAPH YOU WILL FIND THAT WHEN X=6 Y=8
THE ANSWER IS 8.
charles walked on a treadmill 16 3/4 miles over 4 days. how many miles did he walk per day. write the answer as a simplified fraction or mix number
Please help me with this problem i am not sure if what I calculated is correct please help.Let f(x)=12x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)? Enter your answer in the box.g(x) = ---------
SOLUTION
The given equation is
[tex]f(x)=\frac{1}{2}x^2+4[/tex]Recall the definition of vertical stretch
vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1
For a vertical stretch of a scale factor of 4 on f(x) g(x) will be
[tex]g(x)=4(\frac{1}{2}x^2+4)_{}[/tex]Expand the bracket
[tex]g(x)=2x^2+16[/tex]Therefore, the answer is
[tex]g(x)=2x^2+16[/tex]Help please thanks please. Solve for the value of d to the nearest tenth place
d = √74
d = 8.6 (to the nearest tenth place)
Explanations:Given the expression to calculate the distance between the coordinates (-2, 1) and (5, -4) as shown:
[tex]d=AB=\sqrt{(5-(-2))^2+(-4-1)^2}[/tex]Simplify
[tex]\begin{gathered} d=\sqrt{(5+2)^2+(-5)^2} \\ d=\sqrt{7^2+5^2} \\ d=\sqrt{49+25} \\ d=\sqrt{74} \\ d\approx8.6 \end{gathered}[/tex]Hence the simplified form of the expression is √74 or 8.6
sovle the equation 8x-11=9x+2
Given the equation:
[tex]8x-11=9x+2[/tex]To solve this equation for x, the first step is to pass the x-term to the left side of the equation and the number to the right side. For this, you have to apply the opposite operation to both sides of the equal sign, that is, to subtract 9x and to add 11:
[tex]\begin{gathered} 8x-9x-11=9x-9x+2 \\ -x-11=2 \end{gathered}[/tex][tex]\begin{gathered} -x-11+11=2+11 \\ -x=13 \end{gathered}[/tex]Note that the x-term is negative, but the objective is to determine the value of x, so we have to multiply it by (-1) to reverse its sign, and to keep the equality valid, you have to multiply both sides of the equation by (-1)
[tex]\begin{gathered} (-1)(-x)=(-1)\cdot13 \\ x=-13 \end{gathered}[/tex]The Earth has an eccentricity of 0.017. Which of the three ellipses that you calculated do you think is the most similar in eccentricity to the Earth’s orbit? Why?
SOLUTION
Eccentricity means a measure of how much the deviation of the curve has occurred from the circularity of the given shape.
Of the three ellipses, the eccentricity is
[tex]\begin{gathered} \text{Ellipses 1=0.21} \\ \text{Ellipses 2=}0.4 \\ \text{Ellipses 3=0.64} \end{gathered}[/tex]Ellipses 1 has an eccentricity closer to the eccentricity of the Earth
Hence
Ellipses 1 is the most similar in eccentricity to the Earth's orbit
70) Approximately how many feet tall is thestreetlight?A. 12.8B. 15.4C. 16.8D. 23.8
The height of the street light represent the opposite side.
The adjacent is 20ft
the angle is 40 degrees
using trigonometry ratio for tangent
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 40^0=\frac{x}{20} \\ \text{where x=height of the stre}etlight \end{gathered}[/tex][tex]\begin{gathered} x=20\times\tan 40 \\ =20\times0.8390 \\ =16.78 \end{gathered}[/tex]Therefore the streetlight is approximately 16.8ft
The right option is C
BRAINLIEST (statistics) (please help fast)
The fuel economies in miles per gallon (mpg) for nine vehicles are listed below.
16, 18, 20, 24, 24, 24, 24, 31, 32
If one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median?
The mean and median will both increase.
The mean will increase and the median will decrease.
The mean will increase and the median will not change.
The mean will decrease and the median will not change.
Considering the concepts of the mean and the median, the correct option regarding the addition of one more vehicle is given by:
The mean will increase and the median will not change.
What are the mean and the median of a data-set?The mean of a data-set is obtained as the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.
Hence, for the given data-set, the mean is:
M = (16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32)/9 = 23.67.
Hence, if we add a value greater than the mean to the data-set, the mean will increase. In this problem, a rate of 40 mpg would be greater than any observation in the data-set, thus also greater than the mean, which would increase. The new mean is shown as follows:
M = (16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40)/10 = 25.3.
The median of a data-set is the middle value of the data-set, the value which 50% of the observations are less than and 50% are greater than. Hence, the addition of an extreme value, such as 40 mpg in the context of this problem, does not change the median of the data-set.
For the original data-set, the median is:
24
As the data-set is divided into two halfs:
First: 16, 18, 20, 24.Second: 24, 24, 31, 32.With the new element, the halfs would be given by:
First: 16, 18, 20, 24.Second: 24, 24, 32, 40.The median would be the mean of the two middle elements of 24, hence:
Median = (24 + 24)/2 = 24.
Since the mean increases and the median remains constant, the third option is correct.
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5. Using p and q below, write the symbolic statement in words. Assume that p and q are true. q: 3x + 2 = 14 p: the value of x is 4
p⇒ q
~p ~q
q→p
~q→ ~p
In order to avoid ambiguity, symbolic logic represents logical expressions by substituting symbols and variables for natural language, such as English. Statements with a truth value, or whether they are true or untrue, are referred to as logical expressions.
How should a symbolic message be written?
A letter, such as p, can represent a whole proposition in symbolic logic. For instance, it might symbolize the fact that a triangle has three sides. The plus sign in algebra connects two numbers to create a third number. In symbolic logic, a sign like the letter V joins two propositions to create a third one.
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is (8, -44) a solution of the equation y = -7x + 6?
The ordered pair (8, -44) is not a solution of the equation
How to determine the true statement?The equation of the function is given as
y = -7x + 6
The possible solution of the equation is given s
(8, -44)
This means that
x = 8 and y = -44
Substitute x = 8 and y = -44 in the equation y = -7x + 6
So, we have the following equation
-44 = -7 x 8 + 6
Evaluate the products
So, we have the following equation
-44 = -56 + 6
Evaluate the sum
So, we have the following equation
-44 = -50
The above equation is false
Hence, the solution is not a solution
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Fred has 5/8 of a pizza left to share with 3 people. If it is split up evenly, how much of the pizza will each person get?
In a circle, the perpendicular bisector of a chord contains the center of the circle.Given : O X with L the 1 bisector of WY.Prove: L contains the center of O X.
All radii of the circle are congruent.Therefore, the radii XW and XY are congruent
[tex]\begin{gathered} XW\cong XY \\ \end{gathered}[/tex]Consider the following equation.
7x +9y = 5y-6
Step 2 of 2: Find the equation of the line which passes through the point (-8,-6) and is perpendicular to the given line. Express your answer in slope-intercept
form. Simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]7x+9y=5y-6\implies 7x+4y=-6\implies 4y=-7x-6 \\\\\\ y=\cfrac{-7x-6}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{7}{4}}x-\cfrac{3}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{-7}\implies \cfrac{4}{7}}}[/tex]
so we're really looking for the equation oif a line whose slope is 4/7 and it passes through the point (-8 , -6)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{4}{7}}(x-\stackrel{x_1}{(-8)}) \implies y +6= \cfrac{4}{7} (x +8) \\\\\\ y+6=\cfrac{4}{7}x+\cfrac{32}{7}\implies y=\cfrac{4}{7}x+\cfrac{32}{7}-6\implies {\Large \begin{array}{llll} y=\cfrac{4}{7}x-\cfrac{10}{7} \end{array}}[/tex]
What is the zero of p(x) = ax-b ?
Given:
[tex]p(x)=ax-b[/tex]Let p(x)=0
[tex]\begin{gathered} 0=ax-b \\ ax=b \\ x=\frac{b}{a} \end{gathered}[/tex][tex]\frac{b}{a}\text{ is the zero of p(x)}[/tex]Determine the slope of the line passing through the points (5,6) and (-5,-1)m=____
GIVEN:
We are given two points on a line and these are;
[tex]A=(5,6),\text{ }B=(-5,-1)[/tex]Required;
We are required to determine the slope of the line passing through these points.
Step-by-step solution;
The slope of a line is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(5,6) \\ \\ (x_2,y_2)=(-5,-1) \end{gathered}[/tex]We can now substitute these into the formula and then simplify;
[tex]\begin{gathered} m=\frac{-1-6}{-5-5} \\ \\ m=\frac{-7}{-10} \\ \\ m=\frac{7}{10} \end{gathered}[/tex]ANSWER:
The slope of the line passing through the given points is;
[tex]m=\frac{7}{10}[/tex]Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /
If the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
Given that the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.
We are required to find the margin of error of Val's data.
Margin of error is basically the difference between the actual data and the calculated data.
Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]
In our case σ=50 and n is 100.
Margin of error=1.96*50/[tex]\sqrt{100}[/tex]
=1.96*50/10
=1.96*5
=9.80
Hence if the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
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9. Higher Order Thinking The table shows
the temperatures of the water in
14 different beakers. What is the average
temperature, rounded to the nearest tenth
of a degree?
Temperatures in Beakers
Temperature 4.5°C 3.7°C 4.3°C 4.1°C 2.9°C
Frequency
3
4
2
3
2
The Average temperature of the given distribution is; 3.3°C
What is the average temperature?When given the values of the input and their frequencies of occurrence, the average mean can be calculated from the formula;
x' = ∑fx/∑f
Thus;
∑fx = ((4.5 * 3) + (3.7 * 4) + (4.3 * 2) + (4.1 * 3) + (2.9 * 2))
∑fx = 13.5 + 14.8 + 8.6 + 12.3 + 5.8
∑fx = 46.4
∑f = 3 + 4 + 2 + 3 + 2
∑f = 14
Thus;
Average temperature = 46.4/14 = 3.3°C
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Evaluate sin 315º without using a calculator.O A. 132DIRO B.B. -12OC, V22O D. - 12
Answer:
Choice D.
Explanation:
Another way to write 315 degrees is
[tex]315-360=-45[/tex]In other words, when measured clockwise, 315 degrees = -45 degrees; therefore, our problem becomes
[tex]\sin 315^o=\sin -45^o[/tex]since
[tex]\sin \theta=-\sin -\theta[/tex][tex]\sin 45=-\sin -45[/tex][tex]\frac{\sqrt[]{2}}{2}=-\sin -45[/tex][tex]\sin -45=-\frac{\sqrt[]{2}}{2}[/tex]Therefore,
[tex]\boxed{\sin 315^o=-\frac{\sqrt[]{2}}{2}}[/tex]which is our answer!
Belinda is altering dance costumes for an upcoming recital. The number of costumes
she can alter varies directly with the amount of time spent working. If Belinda can
alter four costumes in one hour, find the number of costumes she can alter in four
and a half hours.
Answer: c
Step-by-step explanation: the equation asks for the divison of the two equal libruims and u subtract the numeriator by the scound stance
A typical passenger vehicle emits about 4.7 metric tons of carbon dioxide per year. Assuming there are 253 million cars and trucks in the U.S, estimate the total emitted weight of carbon dioxide in the U.S
To estimate this quantity we can multiply the quantities given in the problem:
[tex]253\cdot4.7=1189.1[/tex]The estime total emmited weight of carbon dioxide in the U.S. is about 1189.1 millions of tons
basketball player made 76 out of 100 attempted free throws. What percent of free throws was made?
Percentages measure the frequency of occurrence of a certain event with respect to the occurrence of another event.
This is measured as a division or ratio:
[tex]P=\frac{\text{frequency of event 1}}{frequency\text{ of event 2}}[/tex]The basketball player made 76 out of 100 attempts. Here, our event 1 is the basketball player making a free throw. Event 2 is the player throwing the ball, regardless of its result.
Since he/she made 76 out of 100, the percent is:
[tex]P=\frac{76}{100}=0.76[/tex]The percent is 0.76*100 = 76%
Lin is reading a 47 page book. She read the first 20 pages in 35 minutes. If she continues to read at the same rate will she be able to complete in under an hour? If not, how much more time is needed?
Answer:
No, 40 pages would take 70 minutes.
Step-by-step explanation:
20 more pages would take 35 more minutes which would be 40 pages at 70 minutes, then you will divide your 7 pages left by the 35 minutes it took to read the the first two 20 page sections of the book.
35 min.+ 35 min = 70 min. 35 mins./7 pages = 5 minutes
So it took a total of 75 minutes for Line to read her 47 page book.
please help me!!!!!!
This is a table that models the data correctly, and the percentage is 21.52%.
It's calculate of this way:
[tex]\frac{100}{79}\cdot17=21.52[/tex]What is the slope of the line through the point (4,4p) & (10,12q)?
(hint: Use the slope formula)
Answer: slope =4/3
Step-by-step explanation:
y2 - y1 / x2 - x1
y2 = 12
y1 = 4
12 - 4 / x2 - x1
subtract: 8 / x2 - x1
x2 = 10
x1 = 4
8 / 10 - 4
subtract: 8/6
8/6 simplify to 4/3
The slope is 4/3
What is x^2+x when x = 69?
if x = 69, then x^2+x = 4830
