For example, if there are 5 blue balls and 7 red balls. the ration of the blue balls with the red balls is
[tex]5\colon7[/tex]it can also be written as a fraction :
[tex]\frac{5}{7}[/tex]It is important to put the one that was mentioned first in the numerator. in this case is blue ball, that's why 5 came first. If we are asked what is the ratio of the red balls with the blue balls , then we will have to indicate 7 first. The ratio will have to be
[tex]\begin{gathered} 7\colon5 \\ or \\ \frac{7}{5} \end{gathered}[/tex]The sequence is important.
Miss Davidson ran a sit-up competition among her P.E. students and monitored how many sit-ups each student could do. Number of sit-ups Number of students 76 3 79 5 175 2 X is the number of sit-ups that a randomly chosen student did. What is the expected value of X? Write your answer as a decimal.
Let the total number students be s. Then
s = 3 + 5 + 2= 10
x | Number of students(n) | Pr(x) | xPr(x)
---------------------------------------------------------------------------------
76 | 3 | 0.3 | 22.8
---------------------------------------------------------------------------------
79 | 5 | 0.5 | 39.5
--------------------------------------------------------------------------------
175 | 2 | 0.2 | 35
--------------------------------------------------------------------------------
[tex]\sum \text{xPr(x) = 22.8 + 39.5 }+\text{ 35 = 97.3}[/tex][tex]\text{ The expected value is }\sum \text{xPr(x)}[/tex]Therefore, the expected value of x is 97.3
4.74 do you own a tablet? a study20 conducted in june 2015 examines ownership of tablet computers by us adults. a random sample of 959 people were surveyed, and we are told that 197 of the 455 men own a tablet and 235 of the 504 women own a tablet. we want to test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women. state the null and alternative hypotheses, and define the parameters. give the notation and value of the sample statistic. in the sample, which group has higher tablet ownership: men or women? use statkey or other technology to find the p-value.
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
Sample proportion for men who own tablets ≈0.433
Sample proportion for women who own tablets ≈0.466
p value of the test is 0.3320.
Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.
Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
The notations for the sample statistic are p p1 p2
Pooled proportion p = [tex]\frac{x_{1}+x_{2} }{n_{1}+n_{2} }[/tex]= 197+235/455+504
≈ 0.45
Sample proportion for men who own tablets,
p1 = [tex]\frac{x_{1} }{n_{1} }[/tex]= 197/455
≈0.433
Sample proportion for women who own tablets,
p2 = [tex]\frac{x_{2} }{n_{2} }[/tex] = 235/506
≈0.466
Since p1<p2 women group has higher tablet ownership.
Sample statistic, p1-p2
= 0.433-0.466
p value of the test is 0.3320.
What is Null hypothesis?In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.
In probability and statistics, the null hypothesis is the general statement or default state that zero or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until other evidence is presented to disprove the hypothesis.
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With his new trainer, jacob now bikes at an average speed of 21 mph. that is 5% faster than he averaged with his old trainer. how fast did he bike, on average, before training with the his new trainer?
The average before training with new trainer is 20 mph.
Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer
Keep the values in formula to find the average speed with old trainer.
21 = 5/100x + x
Multiplying the equation with 100
2100 = 5x + 100x
Performing addition
105x = 2100
Shifting 105 to Right Hand Side of the equation
x = 2100 ÷ 105
Performing division on Right Hand Side of the equation
x = 20
Thus, average speed with old trainer was 20 mph.
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a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error. the sample standard deviation. the estimated standard error. the population mean. the population standard deviation.
A parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is the population mean.
What is meant by population mean?The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The μ sign stands for the population mean.
The average calculated from the entire group, distribution, or population is known as the population mean. It is calculated by dividing the sum of all population variables by the total population of variables. Here, μ exists the population mean. ∑X exists the sum of all the observations in the population.
The population mean is a quantity that expresses the population's overall degree of individual variation, which is often unknown.
Therefore, the correct answer is option c) the population mean.
The complete question is:
a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error.
a) the sample standard deviation.
b) the estimated standard error.
c) the population mean.
d) the population standard deviation.
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Find the value of $x$ so that the ratios are equivalent.
$3$ to $2$ and $x$ to $18$
x=27
I think it's because if 3 is to 2 then 18+9=27. which means 27 is to 18.
Martin, a carpenter wants to make a spice rack for the kitchen. He cuts a 16.24 feet long plank into 5 pieces of equal length. What is the length of each piece of wood ? Round to the nearest hundredth.
Solution
For this case we can solve the problem with the following operation:
[tex]\frac{16.24ft}{5}=3.248ft[/tex]And rounded the answer we got 3.25 ft
16.24*100 = 1624
5*100 = 500
And we can do this:
1624/500 = 812/250 = 406/125
003
_____
125 / 406
-0
____
-40
-0
____
406
-375
_____
31
(MULTIPLE CHOICE) Write an expression that would represent the perimeter of a rectangle with a width of 10n and a length of 4.
A) 10n + 4 + 10n + 4
B) 10n + 4
C) 4(20n) (this is multiplication)
D) 10 + 4 + 20n + 4
Select which of these transformations is hardest for you to write using algebraic notation.
The graph that is hardest to write the transformation using algebraic notation is the second top graph counting from left to right
What are graph?A graph is a pictorial representation of data
What is transformation?A transformation is a movement that can be represented in a cartesian plane.
There several types of movement involved in transformation, some of them are:
TranslationReflectionDilation and so onThe first top graph counting from the left is a translation to the left.
The first graph at the bottom counting from the left is a translation downwards
The next bottom graph is reflection along x axis and translation downwards
The most difficult which is the second at the top counting from left involves dilation.
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The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
Using the Pythagorean Theorem formula, the measurement of the unknown side (base) is 12 units.
How can the measurement of the unknown side of a right triangle be determined?According to the Pythagorean Theorem formula, c² = √a²+b², where c = hypotenuse, a = perpendicular, and b = base.
The hypotenuse is the longest side of a right triangle.
The shortest side is the perpendicular (adjacent side) while the other side is the base (opposite side).
Since the hypotenuse is given as equal to the square root of perpendicular squared and the base squared, we can compute the base, unknown side, using the following Pythagorean Theorem formula.
c² = √a²+b²
The perpendicular (shortest side) of a right triangle = 5
The hypotenuse (longest side) = 13
c² = √a²+b²
169 = √5²+b²
169 = √25 + b²
The base (unknown side):
b² = 169 - 25
b² = 144
The square root of √144 = 12
b = 12
Thus, the unknown side of the right triangle is the base, measuring 12 units.
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The length of the unknown side is 12 units, which is the base of the right triangle.
The right triangle's perpendicular (shortest side) = 5 units
The right triangle's hypotenuse (longest side) = 13 units
According to the Pythagorean Theorem,
H² = P² + B², Where H = hypotenuse, P = perpendicular, and B = base.
As per the given question, here H = 13 and P = 5
Substitute the values of H = 13 and P = 5 in the Pythagorean Theorem,
(13)² = (5)²+ B²
169 = 25 + B²
B² = 169 - 25
B² = 144
B = √144
B = 12 units
Therefore, the length of the unknown side is 12 units,
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In the triangle below, suppose that mV = (x - 2)",mW = (x - 2)°, and m ZX=(4x+4)*Find the degree measure of each angle in the triangle.(x - 2)(4x + 4)m ZV =Х5?m ZW =001Xm 2x =(x - 2)°
SOLUTION
Consider the image given below.
From the image above,
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \angle W=(x-2)^0 \\ \angle X=(4x+4)^0 \end{gathered}[/tex]To find the measures of each angle, we need to obtain the value of small x in the diagram.
Applying the rule: Sum of angle in a triangle is 180 degrees
[tex]\angle V+\angle W+\angle X=180^0[/tex]Then substitute the given expression, we have
[tex]\begin{gathered} (x-2)^0+(x-2)^0+(4x+4)^0=180^0 \\ Then \\ x-2+x-2+4x+4=180^0 \end{gathered}[/tex]Collect like terms and add
[tex]\begin{gathered} x+x+4x-2-2+4=180^0 \\ 6x-4+4=180^0 \\ \text{then} \\ 6x=180 \end{gathered}[/tex]Divide both sides by 6, we have
[tex]\begin{gathered} \frac{6x}{6}=\frac{180}{6} \\ hence \\ x=30 \end{gathered}[/tex]hence, x=30
Then substitute the value of x to obtain the measure of each angles.
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \text{Then x=30} \\ \angle V=30-2=28^0 \end{gathered}[/tex]Since the triangle is an issoceles triangle, then
[tex]\angle W=28^0[/tex]Hence
[tex]\begin{gathered} \angle X=(4x+4)^0 \\ \angle X=(4\times30+4)^0=(120+4)=124^0 \\ \text{hence} \\ \angle X=124^0 \end{gathered}[/tex]Therefore
Answer : ∠V= 28°, ∠W=28°, ∠X=124°
gmm
2
#x²
13
O
1
2
ABC
3
5x+2
3x + 40
Find the measure of angle 2.
label optional
1
2 3 4
5 6 78 9
XY Z<
7
VI
Xi
+
8
=
V
Answer: [tex]\angle 2=83^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]
This means that [tex]5x+2=3x+40=97[/tex].
Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]
I need help fast with my math homework.
Answer:15 twice
Step-by-step explanation:
ramone scores 40 on his history test and 40 on his chemistry test. the class means for both tests is 30. the standard deviation for the history test is 10 and the standard deviation for the chemistry test is 5. on which test did he do better in relation to his peers and why?
Ramones’s Chemistry test was much better as it has higher Z-Score than history
For History test, Test score (x) = 40
Mean (μₓ) = 30, Standard deviation (σₓ) = 10
For Chemistry test, Test score (Y) = 40
Mean (μ) =30, Standard deviation (σ) =5
Ramones’s Z-score for History test is given by,
Z-Score = (x-μₓ)/σₓ =(40-30)/10 = 1
Ramones’s Z-score for chemistry test is given by,
Z-Score = (y-μ)/σ =(40-30)/5 = 2
Thus, Ramones’s Chemistry test was much better, because Chemistry test has higher z-score.
Difference in the mean score (α) =μₓ -μ =0
Difference in Z-Score= Z- Zₓ =1
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Subtract and simplify:
PLEASE HELP ASAP
5 1/3 − 4 5/6 = _____
Responses
A 1 2/3
B 1 4/6
C 1/2
D 3/6
Answer:
C. 1/2
Hope this helps!
[tex]\boxed{\boldsymbol{\sf{5\frac{1}{3}\times4\frac{5}{6} }}}[/tex]
Multiply 5 and 3 to get 15.
[tex]\boxed{\boldsymbol{\sf{\dfrac{15+1}{3}-\left(\frac{4\times6+5}{6}\right) }}}\boldsymbol{\longmapsto \ Add \ [15+1]}[/tex]
[tex]\boxed{\boldsymbol{\sf{\dfrac{16}{3}-\left(\frac{4\times6+5}{6}\right) }}}\boldsymbol{\longmapsto \ Multiply \ [4*6+5]}[/tex]
[tex]\boxed{\boldsymbol{\sf{\dfrac{16}{3}-\left(\frac{29}{6}\right) }}}[/tex]
Convert fractions prior to fractions with equal denominators.
[tex]\boxed{\boldsymbol{\sf{\frac{32}{6}-\dfrac{29}{6}=\frac{32-29}{6}=\frac{3}{6}=\dfrac{3\div3}{6\div3}=\frac{1}{2} }}}[/tex]
The answer is 1/2, therefore the alternative is correct is option C.3/4 - (-1/2) as a fraction
Answer:1/4
Step-by-step explanation:
i don't get it could you please help me? also please could it be quick because I have soccer practice too
The number of cups of bananas is represented by x
The number of cups of strawberries is represented by y
Note that:
[tex]\begin{gathered} 1\frac{2}{25}\text{ = }\frac{27}{25} \\ 5\frac{2}{5}=\text{ }\frac{27}{5} \\ 2\frac{18}{25}=\text{ }\frac{68}{25} \\ 13\frac{3}{5}=\text{ }\frac{68}{5} \end{gathered}[/tex]27/5 cups of strawberry is used for 27/25 cups of banana
1 cup of strawberry is used for x cups of banana
x = 27/25 ÷ 27/5
x = 27/25 x 5/27
x = 1/5
1/5 cups of banana is used for 1 cup of strawberry
Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:
y = 5x
where k = 5
The constant of proportionality = 5
For Problems 3–6, find the opposite of the number.4.5
ANSWER
-4.5
EXPLANATION
We want to find the opposite of the number 4.5
The opposite of a number is the number that is the same distance from 0 on the number line but on the other side.
So, if the number is on the right hand side, its opposite is on the left hand side.
In simpler terms, the opposite of a number is the negative of a number.
So, the opposite of 4.5 is -4.5.
Line m passes through points (9, 9) and (6, 1). Line n passes through points (10, 7) and (1, 15). Are line m and line n parallel or perpendicular?
Answer:
Step-by-step explanation:
Slopes of parallel lines are the same. ( [tex]m_{1}[/tex] = [tex]m_{2}[/tex] )
Slopes of two perpendicular lines are opposite reciprocals. ( [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1 )
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
(9, 9)
(6, 1)
[tex]m_{m}[/tex] = [tex]\frac{1-9}{6-9}[/tex] = [tex]\frac{8}{3}[/tex]
(10, 7)
(1, 15)
[tex]m_{n}[/tex] = [tex]\frac{15-7}{1-10}[/tex] = - [tex]\frac{8}{9}[/tex]
Lines m and n neither parallel, nor perpendicular.
Ryan Pick 6 1/2 cups of berries from his garden he use 3 3/8 cups of to make fruit salad if he needs 3 cups of berries to make a pie does Ryan have enough very stuff to also make a pie?
We will simply subtract 3 3/8 from 6 1/2
That is;
6 1/2 - 3 3/8
= 3 4-3/8
=3 1/8
The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie
need help on this, thanks
The value of question are 65+[tex]\underline{115}[/tex]=180, [tex]11x+\underline{48}=180^o[/tex], [tex]11x=\underline{132}[/tex] and [tex]x=\underline{12}[/tex].
In the given question we have to find the value of missing term.
(1) 65+......=180
(2) 11x+.......=180
(3) 11x=.........
(4) x=........
To solve this question we have to use some theorem.
Firstly solving the first question.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So from the diagram
[tex]65+z=180^o[/tex]
Subtract 65 on both side
[tex]65+z-65=180^o-65[/tex]
[tex]z=115[/tex]
Hence, 65+[tex]\underline{115}[/tex]=180.
Now finding the value of second question.
Using Alternate Exterior Angles Theorem
According to theorem the angle beside 11x - 17 is 65.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So 11x-17+65=180[tex]^o.[/tex]
Simplifying
So [tex]11x+\underline{48}=180^o[/tex]
Now finding the value of third question.
From the second question answer we get [tex]11x+{48}=180^o[/tex]
Now solving this equation to find the value of 11x
Subtract 48 on both side
[tex]11x+{48}-48=180^o-48[/tex]
[tex]11x=132[/tex]
Hence, [tex]11x=\underline{132}[/tex]
Now solving the fourth question.
To find the value of fourth question we further simplify the answer of third question.
[tex]11x=132[/tex]
Divide by 11 on both side
[tex]\frac{11}{11}x=\frac{132}{11}[/tex]
[tex]x=12[/tex]
Hence, [tex]x=\underline{12}[/tex]
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2
Select the correct answer.
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?
A.
It is the graph of y = x where the slope is decreased by 8.
B.
It is the graph of y = x translated 8 units up.
C.
It is the graph of y = x translated 8 units to the left.
D.
It is the graph of y = x translated 8 units down.
Answer:
the answer of a question is option A
Write the sentence as an equation.
312 equals the total of 380 and p
Answer:
P+380=312
Step-by-step explanation:
The total, meaning addtion, and equals meaning equals sign. P+380=312
1.Tanisha solved the equation below by graphing a system of equations.log: (5x) = log5 (2x + 8)What are the two equations in the system of equations that could be used to approximate her solution?(Do your best to type out the two equations for the system.)Yi =Y2 =2. What is the approximate solution (x -value) for her system of equations? And where on the graph can tanisha find her solution to the system?
Part 1.
Since we have the equation
[tex]\log _3(5x)=\log _5(2x+8)[/tex]the equations which can be used to approximate the solutions are:
[tex]\begin{gathered} y_1=\log _3(5x) \\ y_2=\log _5(2x+8) \end{gathered}[/tex]Part 2.
Let's make the graph of the 2 equations. The graph is
The approximate solution is given by the intersection point of the 2 graphs, which is the point ( 0.957 , 1.425). Then x-value corresponding to the solution is x= 0.957.
a researcher is told that the average age of respondents in a survey is 49 years. she is interested in finding out if most respondents are close to 49 years or not. the measure most appropriate to answer this question is:
The measure that would most correctly answer this question is standard deviation.
What is standard deviation?
The standard deviation is measure of how spread out data from mean.
Step-by-step explanation:
Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.
Hence here measures of dispersion fact will be used.
Measures of dispersion are range and standard deviation.
Range is nothing but the difference between maximum and minimum values of the data.
Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.
Therefore the correct option is standard deviation.
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find the measures of the copleentary angles that satisfy each case angles have equal measure
Answer:
The measures of this complementary angles is:
45°
Step-by-step explanation:
Complementary angles sum 90°
∡A + ∡B= 90°
∡A = ∡B
Then:
∡A + ∡A = 90°
2∡A = 90°
∡A = 90/2
∡A = 45°
∡B = 45°
8) A bank pays interest of 11%. Mamuru puts $5000 in the bank.
How much money does he have after:
a) one year?
b) three years?
c) five years?
Answer:
Assuming that the interest Is paid out yearly After one year he would have $5550 After 3 years he would have $6838.16 After 5 years he would have $8425.29
Slope And Rate Of Change
Based on the linear relationship between the ticket numbers and the total cost, the cost of one ticket can be found to be A. $10.50
How to find the cost of one ticket?First, find the rate of change in ticket pricing assuming the number of tickets is x and the total cost is y.
The rate of change is:
= Change in y / Change in x
= (67.50 - 46.50) / (5 - 3)
= $10.50
Then find the y-intercept:
y = Slope(x) + y-intercept
67.50 = 10.50(5) + y-intercept
y-intercept = 67.50 - 52.50
y-intercept = 15
Linear equation is:
Total cost = Rate of change (Tickets) + y-intercept
A single ticket would cost $10.50 which is the rate of change.
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The required rate of change and slope of the given relationship is $10.50.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope for the linear function is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the table substitute the value in the above equation,
m = [67.50-46.50]/[5-3]
m = 21 / 2
m = 10.50
Thus, the required rate of change and slope of the given relationship is $10.50.
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The number of alligators in a wildlife preserve inLouisiana can be shown with the exponential functionf(0) = 3450(1.04)++! Find the average growth rate ofchange from the 4th year to the 7th year.
Given data:
The given function is f(x)=3450(1.04)^(x+1).
The
Write the equation of the line passing through the point (6,-9) that is perpendicular to the line y=1/2x+11.
The line that is perpendicular to the equation of a line given is y = -2x + 3
What is the equation of a perpendicular line?The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.
For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).
To find an equation of a line;
Identify the slope.Identify the point.Substitute the values into the point-slope form, y − y₁ = m ( x − x₁) . y − y₁ = m (x − x₁) .Write the equation in slope-intercept formThe equation of the line can be modified into y - y₁ = m(x - x₁)
substituting the values into the equation above gives y = -2x + 3
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Which subatomic particles are located in the nucleus of an He-4 atom?
The sub-atomic particles located in the nucleus of an He^4 atom are 2 protons and 2 neutrons.
Helium belongs to double-electronic species, unlike alpha-particles which are devoid of electrons. The two electrons of Helium are accommodated in the 1s orbital, outside the nucleus.
Nucleons are always present in the nucleus of various elements. Nucleons collectively refer to protons and neutrons. In this case, 2 protons and 2 neutrons reside in the nucleus.
The number of protons is always equal to the atomic number of the element. The number of neutrons is always equal to the difference between the mass number and the atomic number of the element.
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