Answer:
The farmer has 4 cows and 15 chickens.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of cows
y is the number of chickens.
A farmer has a total of 21 cows and chickens altogether
This means that x + y = 21.
The animals have 54 legs
A cow has four legs, while a chicken has 2 legs. So
4x + 2y = 54.
From the first equation:
y = 21 - x
Replacing
4x + 2(21 - x) = 54
4x + 42 - 2x = 54
2x = 12
x = 6
y = 21 - x = 21 - 6 = 15
The farmer has 4 cows and 15 chickens.
The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. x 0 1 2 3 4 5 P(x) 0.09 0.26 0.29 0.20 0.09 0.07 Find P(2 or fewer).
Answer:
probability (x ≤2) = 0.64
Step-by-step explanation:
P(2 or fewer) = probability of 2 or fewer
probability of (2 or fewer) = probability (x ≤2)
probability of (2 or fewer) = probability when x is 0 + probability when x is 1 + probability when x is 2
probability of (2 or fewer) = probability (x =0) + probability of (x =1 ) + probability (x= 2)
probability of (x=0) = 0.09
probability of (x=1) = 0.26
probability of (x =2) = 0.29
probability of (2 or fewer) = 0.09 + 0.26 + 0.29 = 0.64
probability (2 or fewer) = probability (x ≤2) = 0.64
Answer:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
Step-by-step explanation:
For this case we have the following probability distribution:
x 0 1 2 3 4 5
P(x) 0.09 0.26 0.29 0.20 0.09 0.07
And we want to find the following probability:
[tex] P(X \leq 2)[/tex]
And we can find the probability like this:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
please help me, I'll give brainly
Answer:
Hai
It should be the fourth option. 44/20<45/20
Because firstly we should bring them same to make calculation.
im bringing them denominator to 20.
for 11/5, i should multiply both with 4.
11×4 = 44/20 = 5 × 4
for 9/4 ill multiply both with 5.
9×5 = 45/20 = 5 × 4
good luck(:
A builder makes drainpipes that drop 1 cm over a
horizontal distance of 30 cm to prevent clogs. See the
diagram below, which is not drawn to scale:
A certain drainpipe needs to cover a horizontal distance
of 700 cm
What is the length l of this drainpipe?
Round your answer to the nearest tenth of a centimeter
cm
Answer:
700.4 cm
Step-by-step explanation:
This involves two similar triangles.
Both triangles are right triangles.
One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.
(1 cm)^2 + (30 cm)^2 = c^2
c^2 = 901 cm^2
c = sqrt(901) cm
The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [sqrt(901) cm]/x
3/70 = sqrt(901) cm/x
3x = 70 * sqrt(901) cm
x = 70 * sqrt(901) cm/3
x = 700.4 cm
Answer: 700.4 cm
The length of drainpipe is 700.4 cm.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
One has legs measuring 1 cm and 30 cm.
Using Pythagorean theorem.
(1 cm)² + (30 cm)² = c²
c² = 901
c =√901 cm
Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [√(901) cm]/x
3/70 = √(901) cm/x
3x = 70 x √(901) cm
x = 700.4 cm
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Data was collected on the heights of boys at 12 and 24 months of age. The data is summarized in the following boxplots. Is there more variation in the boys' heights at 12 months or 24 months? Explain how you can tell from the boxplots.
A. There is more variation in height at 24 months. The whiskers are more symmetric for the 24-month data, indicating greater spread in the data.
B. There is more variation in height at 12 months. The box length is smaller, indicating a smaller interquartile range and greater spread in the data.
C. There is more variation in height at 12 months. The whiskers are less symmetric for the 12-month data, indicating greater spread in the data.
D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data
Answer:
D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data
Step-by-step explanation:
One easy way we can easily tell about the spread and variation data sets is by considering the length of the box in the box plot.
The length of a box plot represents the interquartile range of a data set. The longer the box length, the more the variation and spread there is in the data.
Therefore, considering the diagram of the box plots attached below, the box length for length of boys at 24months is longer than that of the box length of heights of boys at 12 months.
The longer box lengths for heights of boys at 24 months indicates a larger interquartile range compared to that of heights of boys at 12 months. This larger interquartile range implies that, there is more variation in heights at 24 months.
Therefore, the correct option is "D. There is more variation in height at 24 months. The box length is longer, indicating a larger interquartile range and greater spread in the data."
How many yards are in 108 inches?
Answer:
3 yards
Step-by-step explanation:
Divide inches by 36
[tex]108/36\\=3yards[/tex]
Answer:
[tex]3 \: \: yards[/tex]
Step-by-step explanation:
[tex]1 \: \: yard = 36\: \: inches \\ yard \: \: x = 108 \: \: inches[/tex]
So,
[tex] 1 = 36 \\ x = 108 \\ \\ cross \: \: \: multiple \\ \\ 108 = 36x \\ \frac{108}{36} = \frac{36x}{36} \\ x = 3 \: \: yards[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A laptop computer consumes about 20 watts of electricity per hour when operating. At 10 cents per kilowatt-hour, how much does a laptop cost to operate for 5 hours?
Step 1:
Convert the electricity per hour in kilowatts,
Electricity per hour = 20 watts
=20/1000 kilo,watts
Step 2:
The electricity consumes in 5 hour is ,
Electricity in 5 hour = 5x 20/1000 kilo watts.
Obtain the cost as,
=5x20/1000x10
=1 Cent
Answer: =1 Cent
Please mark brainliest
Hope this helps.
The cost of the energy consumed by the laptop for the 5 hours period is 5 cents.
Given:
rate of energy consumption of the laptop, R = 20 Watts per hour
time of operation of the laptop, t = 5 hours
cost of energy consumption, c = 10 cent per kWh
To find:
the cost of the energy consumed by the laptop for the 5 hours periodThe energy consumed by the laptop in kWh is calculated as;
[tex]Energy = Power \times time \\\\Energy = (\frac{20 \ W}{hr} \times 5 \ hr) \times 5\ hr\\\\Energy = (100 \ W) \times ( 5 \ hr)\\\\Energy = (0.1 \ kW) \times (5 \ hr)\\\\Energy = 0.5 \ kWh[/tex]
The cost of consuming 0.5 kWh is calculated as;
[tex]Cost = energy \ rate \ \times \ energy \ consumed \\\\Cost= \frac{10 \ cent}{kWh} \times 0.5 \ kWh\\\\Cost = 5 \ cents[/tex]
Thus, the cost of the energy consumed by the laptop for the 5 hours period is 5 cents.
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Compare 7/8 with 14/16 using ( <, >, =).
A. 7/8= 14/16
B.7/8< 14/16
c.7/8>1446
D. none of the above
Answer:
A
Step-by-step explanation:
multiply 7/8 by 2/2 to get 14/16. they are equal
(1 1 6 − 7 18 )÷2.8 0.5+ 1 18
Step-by-step explanation:
(116-718) /(2.805+118) [as, there cannot be two decimals in one numbers
=-602/120.805
=0.498
Which expressions have the same solution as
Check all that apply.
-4(6)?
04(-6)
4(-6)
6(-4)
-8(2)
12(-2)
Answer: B C E
Step-by-step explanation:
Which undefined term is used to define an angle?
O line
O plane
opoint
O ray
Answer:
A point would be used as the undefined term
A study by Consumer Reports showed that 64% of supermarket shoppers believesupermarket brands to be as good as national brands. A manager of a local storebelieves that the percentage is higher in his store. She asks a random sample of145 shoppers whether they believed that supermarket brand ketchup was as goodas the national brand ketchup. Out of the 145 shoppers asked, 89 believed the supermarket brand was as good as the national brand. Use α= 0.05 significancelevel and conduct a hypothesis test.
Answer:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
Step-by-step explanation:
Information given
n=145 represent the random sample taken
X=89 represent the number of people who believed the supermarket brand was as good as the national brand
[tex]\hat p=\frac{89}{145}=0.614[/tex] estimated proportion of people who believed the supermarket brand was as good as the national brand
[tex]p_o=0.64[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true proportion is less than 0.64, the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.64[/tex]
Alternative hypothesis:[tex]p < 0.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
Three angles are given; Start with angle measures 80,40, and 60. try other sets of angles such as 20, 120, and 40. try three measures that dont add up to 180
Answer: 30, 60 and 80
Step-by-step explanation:
measures 80,40, and 60. And sets of angles such as 20, 120, and 40 will make two different triangles.
To try three measures that dont add up to 180 will never make a triangle.
One of them can be 30, 60, 80
What type of polynomial is P(x) = 7x3 + 2x2 – 3x4?
Answer:
quartic
Step-by-step explanation:
p(x) = 7 x^3 + 2 x^2 - 3 x^4
The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 3, 2, and 4.
The degree of the polynomial is the highest degree of any of the terms; in this case, it is 4.
5)
Calculate the ratio to the nearest hundredth.
-
RATIO
U
DIAMETER (d) CIRCUMFERENCE (C)
20 in.
62.83 in.
är
liliom
DE
10 in.
31.41 in.
6
in.
18.84 in.
2
in.
6.28 in.
1
in.
3.14 in.
0
-
Complete
A
16% Complete
earch
'o
e
Answer:
Answer for (a) to (e) = 0.32
Calculate the ratio to the nearest hundredth.
Find the Ratio of Diameter (d) and circumference (C)
Step by step explanation:
In order to determine the ratio we must know the formula for the circumference of a circle. Then relate it to the diameter.
But since we have been the value if both circumference and diameter, we would just calculate the ratio.
Circumference of a circle = 2πr
Where d = diameter = 2r
Circumference = πd
a) d = 20 in.
C = 62.83 in.
Ratio of Diameter (d) and circumference (C) = d:C
= 20/(62.83)
d:C = 0.32
b) d=10 in.
C =31.41 in.
d:C = 10/(31.41)
d:C = 0.32
c) d =6 in.
C =18.84 in.
d:C = 6/(18.84)
d:C = 0.32
d) d= 2 in.
C = 6.28 in.
d:C = 2/6.28
d:C = 0.32
e) d = 1 in.
C = 3.14 in.
d:C = 1/3.14
d:C = 0.32
The above answers indicate that the ratio of a circumference of a circle to its diameter = d/C = d/(π×d)
= 1/π = 0.32
Find the mode of the following data:
18, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20
O A. 13
OB. 10
O c. 16
D. 14
SUBMIT
10..................
A 3650-year-old wooden chest is found by archaeologists. What percentage of the original Superscript 14 Baseline Upper C would you expect to find in the wooden chest? (Recall that the decay constant for Superscript 14 Baseline Upper C is 0.00012.)
Answer:
64.5%
Step-by-step explanation:
Initial amount N° = ?
Remaining amount after decay = N = ?
k = decay constant = 0.00012 [tex]yr^{-1}[/tex]
t = time = 3650 year
fraction remaining will be N/N°
From the decay equation, N = N°[tex]e^{-kt}[/tex]
N/N° = [tex]e^{-kt}[/tex]
N/N° = [tex]e^{-0.00012 x 3650 }[/tex]
N/N° = [tex]e^{-0.438}[/tex]
N/N° = 0.645 = 64.5%
The distance y (in miles) that a car travels on a highway in x minutes is represented by the equation y=1.1x. The graph shows the distance that a bus travels. Find the speed of each vehicle. Which vehicle is traveling faster?
Answer:
car = 1.1 mi/min
bus = 1.05 mi/min
car travels faster
Step-by-step explanation:
recall that speed is given by the gradient (i.e slope) of a distance vs time graph or equation.
for the car:
equation is y = 1.1x
recall that for an equation in the form y = mx + b, slope = m
if we compare the given equation to the general equation, it is clear that
speed of car = slope = m = 1.1 miles/min (answer)
for the bus,
we are given 2 points (2,2.1) and (4,4.2)
if we apply the formula for slope (see attached for reference)
slope, m
= (4.2 - 2.1) / (4 - 2)
= 2.1 / 2
= 1.05 mi/min= speed of bus (answer)
comparing the 2 speeds, we can see that the car has the higher speed (travels faster).
Answer:
Car:1.1
Bus:1.05
Car is going faster.
Step-by-step explanation:
This is right. I got it right on Big Ideas Math (Pre-Algebra)
What’s the correct answer for this?
Answer:
cats constitute the same fraction of animals adopted as not adopted
(i am actually not that sure)
Answer:
a
Step-by-step explanation:
as mamy cats as dogs are addopted
PLZ HURRRY!!!!! What is the circumference of the circle
Answer:
40.192
Step-by-step explanation:
C=D(pi)
D=6.2*2
C=12.8*3.12
C=40.192
Answer:40.192
Step-by-step explanation:the formula for a circumference if a circle is C=2•3.14•r^2 fill in for r and calculate for your answer
The Senator of Azenator State, is worried about the rising numbers in high blood pressure related deaths in his Jurisdiction and wants an end to this canker. A reputable medical research officer has claimed that, the situation is probably as a result of the ageing population of his State. The blood pressures, Y (mmHg), and Ages, X (years) of 10 hospital patients were sampled from Azenator State and summarized below. Patient A B C D E F G H I J Age (X) in Years 20 25 50 30 45 60 10 15 35 70 BP(Y) in (mmHg) 80 85 125 90 100 135 80 70 100 140 NB: Approximate to 2 decimal places Use the table to answer the questions that follow; i) Calculate the product moment correlation coefficient for the data and interpret your result. (3 Marks) ii) If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer. (3 Marks) iii) Give a reason to support fitting a regression model of the form = + + , where (a) is the y-intercept or constant, (b) is the slope of the function, (y) is the blood pressure of a patient, (X) is the age of a patient and is the error term. (3 Marks) iv) From the model specified in (iii), estimate the values of (a) and (b) and interpret the values (4 Marks) v) What is the blood pressure of an infant at birth? (2 Marks) vi) Predict the blood pressure of a patient who is 90 years old. (2 Marks) vii) Estimate the coefficient of determination and interpret your result.
Answer:
Step-by-step explanation:
Hello!
Given the variables:
Y: Blood pressure of a hospital patient (mmHg)
X: Age of a patients (years)
You have to analyze the claim that the rising numbers in high blood pressure related deaths is associated with the aging of the State's population.
i)
[tex]r= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{\sqrt{[sumX^2\frac{(sumX)^2}{n} ]+[sumY^2-\frac{(sumY)^2}{n}] } }[/tex]
To calculate the correlation coefficient you need to do several additional calculations.
n= 10
∑Y= 1005 mm Hg; ∑Y²= 106475 mmHg²
∑X= 360 years; ∑X²= 16500 years²
∑XY= 40425 years*mmHg
[tex]r= \frac{40425-\frac{360*1005}{10} }{\sqrt{[16500\frac{(360)^2}{10} ]+[106475-\frac{(1005)^2}{10}] } }= 0.96[/tex]
The coefficient of correlation is close to 1 and positive, this means that there is a strong positive correlation between these two variables. This means the blood pressure increases as age does.
ii)
If blood pressure increases with age and so does the risk of dying due to a high blood pressure, then the most logical decision to take is to give priority to the old adults.
iii)
The estimated regression is ^Y= a + bXi + ei
a= y-intercept: is the estimated average blood pressure of the patients when age is 0 years.
b= slope: in the modification of the estimated average blood pressure of the patients when age increases 1 year.
ei= residues
The estimated regression model will allow you to analyze and predict the values of blood pressure of patients within the determined range of age.
iv)
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{40425-\frac{360*1005}{10} }{16500-\frac{(360)^2}{10} } = 1.20 \frac{mmHg}{years}[/tex]
X[bar]= 36 years
Y[bar]= 100.50 mmHg
[tex]a= Y[bar] - bX[bar]= 100.50-1.20*36= 57.33 mmHg[/tex]
The estimated regression equation is ^Y= 57.33 + 1.20Xi
57.33mmHg in the estimated average blood pressure of a patient age zero.
1.20 mmHg/years is the modification on the estimated average blood pressure when the age of the patients increases one year.
v)
At birth an infant is zero years old, so according to the regression model, it's blood pressure will be 57.33 mmHg
According to medical parameters 64.41 mmHg is the average blood pressure of a newborn child, as you can see this model is a little off the average but still within acceptable parameters.
vi)
Using the estimated regression equation you can predict the value of blood pressure for a determined age by replacing the value of X in it:
^Y= 57.33 + 1.20*90= 165.33 mmHg
It is predicted that a 90-year-old patient will have a blood pressure of mmHg.
vii)
[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{sumY^2-\frac{(sumY)^2}{n} } = \frac{1.20^2[16500-\frac{(360)^2}{n} ]}{[106475-\frac{(1005)^2}{10} ]} = 0.93[/tex]
93% of the variability of the patients blood pressure is explained by their age under the model: ^Y= 57.33 + 1.20Xi
I hope this helps!
State whether the data described below are discrete or continuous, and explain why. The exact mass (in grams )of food eaten by a person each day nothing Choose the correct answer below. A. The data are continuous because the data can take on any value in an interval. B. The data are continuous because the data can only take on specific values. C. The data are discrete because the data can take on any value in an interval. D. The data are discrete because the data can only take on specific values
Answer:
A. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data surveyed is the exact mass, in grams, of food eaten by each person each day.
This type of data is continous, not discrete. The mass can take any value within the domain of positive real numbers. It represents a physic variable, and they are always continous.
vlumber company is making boards that are 2944.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 25 is made, and it is found that they have a mean of 2941.0 millimeters with a standard deviation of 12.0. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
Step-by-step explanation:
Information provided
[tex]\bar X=2941[/tex] represent the sample mean
[tex]s=12[/tex] represent the standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =2944[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is equal to 2944 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2944[/tex]
Alternative hypothesis:[tex]\mu \neq 2944[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
Sung Lee invests $5,000 at age 18. He hopes the investment will be worth $20,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
19.8%
Step-by-step explanation:
We have the following formula for continuous compound interest:
A = P * e ^ (i * t)
Where:
A is the final value
P is the initial investment
i is the interest rate in decimal
t is time.
The time can be calculated as follows:
25 - 18 = 7
That is, the time corresponds to 7 years. In addition, A is 20,000 for A and P would be 5,000, we replace:
20000 = 5000 * e ^ (7 * i)
20000/5000 = e ^ (7 * i)
e ^ (7 * i) = 4
ln e ^ (7 * i) = ln 4
7 * i = ln 4
i = (ln 4) / 7
i = 0.198
Which means that the rounded percentage will be 19.8% per year
The rate of growth needed to achieve this goal is 22%
A compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where A is the final amount, r is the rate, t is the period, P is the principal and n is the number of times compounded in a period.
Given that A = 20000, P = 5000, t = 7 (25 - 18). hence:
[tex]20000=5000(1+\frac{r}{1} )^{7*1}\\\\4=(1+r )^{7}\\\\\\ln(4)=7\ ln(1+r)\\\\r=0.22[/tex]
Therefore the rate of growth needed to achieve this goal is 22%
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A box of crayons costs $1.75, including tax. Mr. Valentino wants to purchase boxes of crayons for his class and has a $25 budget. Write an inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget
Answer:
1.75x ≤ 25
Step-by-step explanation:
what is the solution of x=2+ sqrt x-2
Answer:
C
Step-by-step explanation:
[tex]x=2+\sqrt{x-2} \\\\x-2=\sqrt{x-2} \\\\(x-2)^2=\pm(x-2) \\\\x^2-4x+4=\pm(x-2) \\\\[/tex]
[tex]x^2-5x+6=0[/tex] OR [tex]x^2+3x+2=0[/tex]
x=2 and 3
Hope this helps!
Answer:
The answer is option 3.
Step-by-step explanation:
Firstly, we have to move the unrelated term to the other side :
[tex]x = 2 + \sqrt{x - 2} [/tex]
[tex]x - 2 = \sqrt{x - 2} [/tex]
Then, you have to get rid of square root by squaring both sides :
[tex] {(x - 2)}^{2} = {( \sqrt{x - 2} )}^{2} [/tex]
[tex] {x}^{2} - 4x + 2 = x - 2[/tex]
[tex] {x}^{2} - 4x + 4 - x + 2 = 0[/tex]
[tex] {x}^{2} - 5x + 6 = 0[/tex]
Next, you have to solve it :
[tex] {x}^{2} - 5x + 6 = 0[/tex]
[tex] {x}^{2} - 2x - 3x + 6 = 0[/tex]
[tex]x(x - 2) - 3(x - 2) = 0[/tex]
[tex](x - 2)(x - 3) = 0[/tex]
[tex]x - 2 = 0 \\ x = 2[/tex]
[tex]x - 3 = 0 \\ x = 3[/tex]
here are 4 fracion labeled a b c d 3/4 5/6 16/25 9/15 order starting from smallest
Answer:
9/15
16/25
3/4
5/6
Step-by-step explanation:
Convert them to decimals then order them
Answer:
16/25, 9/15, 5/6, 3/4
Step-by-step explanation:
16/25
9/15
5/6
3/4
16
To get to Amala's house, Tara walks 4 blocks west (left), then 3 blocks north (up), and
then 2 blocks west. Amala's house has coordinates (9,9). What are the coordinates of
Tara's starting point?
A
B.
C
D
(2,0)
(2,6)
(15,6)
(12, 2)
Answer:
Correct answer is C. (15,6)
Step-by-step explanation:
Let us think of the [tex]xy[/tex] co-ordinates plane. We can move in four directions.
1. North (i.e. upwards) If we move north or upwards the value of y-coordinate will increase.
2. South (i.e. downwards) If we move south or downwards the value of y-coordinate will decrease.
3. West (i.e. left) If we move west or left the value of x-coordinate will decrease.
4. East (i.e. right) If we move east or right the value of x-coordinate will increase.
Let us imagine, the starting coordinate of Tara be [tex](x,y)[/tex]
Let us apply the above 4 directions and the properties in the question statement.
Step 1: Tara walks 4 blocks west (left), x coordinate will decrease by 4.
New coordinates will be [tex](x-4,y)[/tex].
Step 2: Tara walks 3 blocks north (up), y coordinate will increase by 3.
New coordinates will be [tex](x-4,y+3)[/tex].
Step 3: Tara walks 2 blocks west (left), x coordinate will decrease by 2.
New coordinates will be [tex](x-4-2,y+3) \Rightarrow (x-6,y+3)[/tex].
Now Tara is at (9,9)
Comparing the x and y coordinates:
[tex]x-6=9\\\Rightarrow x = 15[/tex]
[tex]y+3=9\\\Rightarrow y = 6[/tex]
So, Tara's starting point is (15,6) hence, option C is correct.
Matt and Chris leave their uncle's house in Phoenix at the same time. Matt drives west on I-60 at a speed of 76 miles per hour. Chris drives east on I-60 at a speed of 81 miles per hour. How many hours will it take them to be 785 miles apart?
Answer:
4 hours.
Step-by-step explanation:
Circular interpolation involves dividing the arc to be generated into segments, and approximating each segment by a straight line. What is the optimum number of segments would you recommend to be used for each arc
Answer:
I would recommend optimum number of six segments for each arc.
Step-by-step explanation:
The optimum number of segments I would recommend for each arc is six. This way, the circle interpolation will divide the arc into six segments, and approximating each segment by a straight line.
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
Answer:
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
Step-by-step explanation:
The question is incomplete:
There is no data from the sample.
We will use the sample [105 107 117 106 110 ] as an example to solve the question.
The mean of the sample is:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(105+107+117+106+110)\\\\\\ M=\dfrac{545}{5}=109[/tex]
The standard deviation of the sample is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(105-(109))^2+(107-(109))^2+(117-(109))^2+(106-(109))^2+(110-(109))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(16)+(4)+(64)+(9)+(1)]}\\\\\\ s=\sqrt{\dfrac{94}{4}}=\sqrt{23.5}\\\\\\s=4.848[/tex]
This is a hypothesis test for the population mean.
The claim is that your team scored an average significantly less than 110 points.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.01.
The sample has a size n=5.
The sample mean is M=109.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.848.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.848}{\sqrt{5}}=2.17[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{109-110}{2.17}=\dfrac{-1}{2.17}=-0.46[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-0.46, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.46)=0.334[/tex]
As the P-value (0.334) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
