Answer:
[tex]x = - \frac{2}{3} \: \: \: y = \frac{14}{3} [/tex]
Step-by-step explanation:
Since we know -7x=y we use the substitution method and plug it in the top equation.
[tex]x + - 7x = 4[/tex]
[tex] - 6x = 4[/tex]
[tex]x = - \frac{4}{6} [/tex]
or x=-2/3
Then plug it back in the the bottom equation
[tex] - 7( \frac { - 2}{3} ) = y[/tex]
y=14/3
• Work out the percentage change to 2 decimal places when £78.98 is increased to £100
Answer:
The total change is £21.02 from the original amount of £78.98. Therefore, the percentage change is directly related to the original amount.
Divide the total change by the original amount to determine the percentage change the new amount represents.
21.02÷78.98=0.15219 which rounds up to two decimal places as 15.22%.
The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test that measures the degree to which Mexican Americans are adapted to Mexican/Spanish versus Anglo/English culture. The range of possible scores is 1.0 to 5.0, with higher scores showing more Anglo/English acculturation. The distribution of ARSMA scores in a population used to develop the test is approximately Normal with mean 3.0 and standard deviation 0.8. A researcher believes that Mexicans will have an average score near 1.7 and that first-generation Mexican Americans will average about 2.1 on the ARSMA scale.
What proportion of the population used to develop the test has scores below 1.7? Between 1.7 and 2.1?
Answer:
The proportion of the population used to develop the test that has scores below 1.7 is 0.063.
The proportion of the population used to develop the test that has scores between 1.7 and 2.1 is 0.0662.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The distribution of ARSMA scores in a population used to develop the test is approximately Normal with mean 3.0 and standard deviation 0.8.
This means that [tex]\mu = 3, \sigma = 0.8[/tex]
What proportion of the population used to develop the test has scores below 1.7?
This is the pvalue of Z when X = 1.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.7 - 3}{0.8}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a pvalue of 0.063
The proportion of the population used to develop the test that has scores below 1.7 is 0.063.
Between 1.7 and 2.1?
This is the pvalue of Z when X = 2.1 subtracted by the pvalue of Z when X = 1.7.
X = 2.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.1 - 3}{0.8}[/tex]
[tex]Z = -1.13[/tex]
[tex]Z = -1.13[/tex] has a pvalue of 0.1292
X = 1.7
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.7 - 3}{0.8}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a pvalue of 0.063
0.1292 - 0.063 = 0.0662
The proportion of the population used to develop the test that has scores between 1.7 and 2.1 is 0.0662.
The expression (x - 0.35x) represents 35% off the cost of item x. How is this equivalent to multiplying x by 0.65?
Answer:
It is equivalent.
Step-by-step explanation:
(x-0.35x) is (Total price-0.35 × the original price)=0.65×
Suppose a math class contains 40 students. There are 18 females (two of whom speak Spanish) and 22 males (two of whom speak Spanish). Give all answers as decimals to at least two decimal places.
What percent of Spanish speaking students are male? Give answer as a decimal.
Answer:
50%.
Step-by-step explanation:
Given that a math class contains 40 students, and there are 18 females (two of whom speak Spanish) and 22 males (two of whom speak Spanish), in order to know the percent of Spanish speaking students that are male with respect to the total Spanish-speaking students, the following calculation has to be made:
2 + 2 = 4
2 / 4 = 0.5
Therefore, the percentage of Spanish speaking students that are male is 50%.
PLEASE HELP GEOMETRY
Answer:
Step-by-step explanation:
[tex]\frac{6}{18+6}= \frac{x}{8 }[/tex]
24x=48
x=2
describe how to obtain the graph of g from the graph of f(x)=
[tex] \sqrt[3]{x} [/tex]
Answer: see below
Step-by-step explanation:
Notes: Given [tex]y=a\sqrt[3]{x-h}+k[/tex]
h: shifts to the right (if positive) or left (if negative)k: shifts up (if positive) or down (if negative)a: is a vertical stretch (if >1) or shrink (if <1)-a: reflection over the x-axis11) h = -1, k = -2
shifts left 1 unit and down 2 units from the parent function
12) h = 1, k = 5
shifts right 1 unit and up 5 units from the parent function
13) k = 1, a = -1
shifts down 1 unit from the parent function and reflects over the x-axis
14) h = -1, k = 5
shifts left 1 unit and up 5 units from the parent function
The function f(x)=3x+K and f(4)=7. Find the value of K and f(2)
Step-by-step explanation:
step 1. f(4) = 3(4) + K = 7 (plug in values)
step 2. K = -5 (subtract 12 from each side)
step 3. therefore f(x) = 3x - 5
step 4. f(2) = 3(2) - 5 = 1 (plug in x= 2)
What is the answer to this?
9514 1404 393
Answer:
cot(θ) = 24/7
Step-by-step explanation:
A suitable calculator can answer this nicely.
__
Perhaps you're expected to remember relevant trig identities.
tan(θ)^2 = sec(θ)^2 -1
cot(θ) = 1/tan(θ)
__
cot(θ) = 1/√(sec(θ)^2 -1)
cot(θ) = 1/√((25/24)^2 -1) = 24/√(25^2 -24^2) = 24/√49
cot(θ) = 24/7
whats warmer -3 or -4 degree celcius
Find the value of x that makes N the Incenter of the triangle
Answer:
um im not 100% but i think 47
Step-by-step explanation:
The value of x for the given triangle is found to be 6.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
Given triangle has N as the incentre.
Which implies that NJ = NL= NK.
Now, apply Pythagoras theorem in ΔANK to obtain,
AN² = AK²+ NK²
=> 37² = 35² + NK²
=> NK²= 37²- 35²
=> NK²= 144
=> NK = 12
Then, As per the question it can be written as,
2x = 12
=> x = 6
Hence, the value of x for the point N to be the incentre is 6.
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The ratio of the measures of the three angles in a tangle 3107. Find the measures of the angles and write them in size order,
largest:
middle
Answer:
27, 90 and 63
Step-by-step explanation:
Given
Ratio of triangle sides
[tex]Ratio = 3 : 10 : 7[/tex]
Required:
The length of each side
Triangles in a triangle add up to 180.
The side with ratio 3 is:
[tex]S_1 = \frac{3}{3 + 10 + 7} *180[/tex]
[tex]S_1 = \frac{3 *180}{20}[/tex]
[tex]S_1 = \frac{540}{20}[/tex]
[tex]S_1 = 27[/tex]
The side with ratio 10 is:
[tex]S_2 = \frac{10}{3 + 10 + 7} *180[/tex]
[tex]S_2 = \frac{10 *180}{20}[/tex]
[tex]S_2 = \frac{1800}{20}[/tex]
[tex]S_2 = 90[/tex]
Lastly:
The side with 7 as its ratio
[tex]S_3 = \frac{7}{3 + 10 + 7} *180[/tex]
[tex]S_3 = \frac{7 *180}{20}[/tex]
[tex]S_3 = \frac{1260}{20}[/tex]
[tex]S_3 = 63[/tex]
Hence, the angles are: 27, 90 and 63
What are the next 3 terms in the sequence 3,6,9,12?
Answer:
15,18,21
Step-by-step explanation:
Answer:
15 18 21
Step-by-step explanation:
its skskskskskksksskskkssksksksk
PLEASE HELP ASAP 20 POINTS
The newly proposed city park is rectangle shaped. Blake drew a scale drawing of the park and used a scale of 1 cm: 20 ft
1) If the width on the scale drawing of the city park is 25 centimeters, what is the actual width of the park?
A) 250 feet
B) 400 feet
C)500 feet
D)750 feet
2) If the width on the scale drawing of the city park is 25 centimeters and the length is 30 centimeters, what is the actual area of the park?
A) 75,000 ft^2
B) 110,000 ft^2
C) 300,000 ft^2
D) 750,000 ft^2
Answer:
a ,c ,b
esa son creo pero nose
The actual dimensions of the rectangular park are 500 cm by 600 cm and actual area of the park is 300,000 ft²
What is scale?A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.
Given that, Blake drew a scale drawing of a rectangle shaped park and used a scale of 1 cm: 20 ft
We need to find the actual width if the width on the scale drawing of the city park is 25 cm, and actual area if the width on the scale drawing of the city park is 25 cm and the length is 30 cm,
a) The given measurement of width in the drawing is 25 cm,
We have,
1 cm = 20 ft
∴ 25 cm = 20 × 25
= 500 ft
b) The given measurement of the width on the scale drawing of the city park is 25 cm and the length is 30 cm,
Actual width = 500 ft
Actual length = 20 × 30 = 600 ft
Area of rectangle = length × width
Actual area = 500 × 600
= 300,000
Hence, the actual dimensions of the rectangular park are 500 cm by 600 cm and actual area of the park is 300,000 ft²
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Use the information given to find a convenient dass width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class with up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.)
8 classes for 75 measurements; minimum value-20; maximum value = 175
class width
class boundaries
Answer:
a)
Class width = 19.375
b)
Class Boundaries are;
19.5 - 39.5, 39.5 - 59.5, 59.5 - 79.5, 79.5 - 99.5, 99.5 - 119.5, 119.5 - 139.5, 139.5 - 159.5, 159.5 - 179.5.
Step-by-step explanation:
Given the data in the question;
Class width = Range / Number of classes
Range = maximum - minimum = 175 - 20 = 155
Number of classes = 8
so,
Class width = 155 / 8 = 19.375
∴ the class limits will be
20 - 39
40 - 59
60 - 79
80 - 99
100 - 119
120 - 139
140 - 159
160 - 179
Low class boundary = Lower class limit - 0.5
Upper class boundary = upper class limit + 0.5
so
Class Boundaries are;
19.5 - 39.5, 39.5 - 59.5, 59.5 - 79.5, 79.5 - 99.5, 99.5 - 119.5, 119.5 - 139.5, 139.5 - 159.5, 159.5 - 179.5.
If Sara can only work 5% of one hour now many minutes of one hour can Sara work?
5% or 5percent can be thought of 5 per 100.
5 per 100 or 5 out of 100 can be written as 5/100 or 1/20.
An hour have 60 minutes and 1/20 of an hour is 60*1/20=3 minutes.
Therefore Sara can work 3 minutes every hour.
Given: y = 12 when x = 7, find: “y” when x = 5.
Answer:
y = 84/5 or 16 4/5
Step-by-step explanation:
12/5 = y/7
cross-multiply to get 5y = 84
y = 84/5
I If x > 0 and x^2-2x-35 = 0, then the value of x^2 is 3
Answer:
x^2 = 49
Step-by-step explanation:
Notice that the polynomial on the left of the equation can be factored out as:
x^2 - 2 x - 35 = (x - 7) (x + 5)
Then the equation: x^2 - 2 x - 35 = = 0
gives two solutions as follows:
(x - 7) (x + 5) = 0 Then either binomial factor must be zero, and therefore, x = 7 or x = -5
Since we are told that x is POSITIVE, the x = 7, and its square is 7^2 = 49.
In a certain year, about 11/5000 of a country’s population were female nursing home residents and about 7/5000 of a country’s population were male nursing home residents. Find the total fraction of the county’s population that was residing in nursing homes that year
Answer:
18/5000 or 9/2500
Step-by-step explanation:
Since we know both male and female nursing home residents, we can just add the two together to find the total.
A train travels at an average speed of 35m/s. workout the time it takes to travel 225km?
Answer:
Step-by-step explanation:
d = rt
225km = 225,000m
225,000 = 35*t
t = 6,428.57 seconds
or 107.14 minutes
or 1 hour and 47 minutes
Solve the following equation for x.
10 = 2 – 4(ar – 3)
OA. -
a
OB.
Oc.
OD.
5
a
Answer:
Options C. -5/a
x =1/a is the solution for the given equation. Option D is correct.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Let's simplify the equation first:
10 = 2 - 4(ax - 3)
10 = 2 - 4ax + 12 (distribute the negative 4)
10 = -4ax + 14 (combine like terms)
Now we can isolate the variable x by subtracting 14 from both sides and then dividing by -4:
10 - 14 = -4ax
-4 = -4ax
x = 1/a
Therefore, the solution to the equation is x = 1/a.
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Two points A and C are on the same level ground as the foot of pole B . The distance between A and C is 40m and A and C are on the same sides of the vertical pole . The distances from the top of the pole D to A and C are 53 and 85 respectively. Find correct to 1 do the distance between the foot of the pole B and the point A.
Answer:
The distance between the pole and point A is 35.2m
Step-by-step explanation:
First, we have to illustrate the problem. I can't draw as of the moment but I'll try my best to describe the drawing as best as I can. You can draw this in a scratch paper to have a better understanding.
In a horizontal line, there is a point A, B, and C.From left going to right, the arrangement of points will be C-A-B.The distance between A and C is 40m.The pole is standing at point B with height h.The tip of the pole or the top most part of the pole is point D.From point D to A, the measurement is 53m.From point D to C, the measurement is 85m.Let's name the distance between A and B as x.Now that you have drawn this. There should be two triangles formed now namely triangle DCB and DAB.
TRIANGLE DCB
By Pythagorean Theorem, we can write an equation for the height of the pole.
[tex]h^{2} = {53}^{2} - {x}^{2} [/tex]
TRIANGLE DAB
By Pythagorean Theorem, we can write an equation for the height of the pole.
[tex] {h}^{2} = {85}^{2} - {(40 + x)}^{2} [/tex]
Since we only have one pole, this means that we can equate the two equations.
[tex] {53}^{2} - {x}^{2} = {85}^{2} - {(40 + x)}^{2} \\ {53}^{2} - {85}^{2} = {x}^{2} - ( {x}^{2} + 80x + 1600) \\ - 4416 = - 80x - 1600 \\ 80x = 4416 - 1600 \\ 80x = 2816 \\ x = \frac{2816}{80} \\ x = 35.2[/tex]
The ratio of sheep to the total number of animals on a local farm is 2:5.
Which of the following is the percent of animals on the farm that are
sheep?
29%
60%
40%
20%
*says the correct answer is 29%
Answer:
40%
Step-by-step explanation:
2:5 is equal to 4:10 or 40%.
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
--> Its not 29% its 40%
hope it helps you,
mark me as the brainliest....
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solve the triangles. Round to the nearest tenth А 7 B 6 C
Answer:
Sure but can you show me the triangle.
Please do all of the attachments, quick. It is due please
First one with the right answer gets brainlest, and I will give extra points please.
1. Only 60% of the students passed a drawing class. 2,000 students took the class. Find out how many students were failures.
Answer:
800 students failed
Step-by-step explanation:
Since 60% passed the class, 40% failed
This means that 40% of the 2,000 students are failures
[tex]\frac{40}{100} (2,000)= 800[/tex]
518489625648789*46548897
Answer:
[tex]2.41351201 *10^2[/tex]
Step-by-step explanation:
hope this helps have a good rest of your day :) ❤
A large discount store wants to determine the average yearly income of its shoppers. A researcher chooses 100 shoppers at random between 1:00 p.m. and 5:00 p.m. on a Saturday to survey. Identify the population.
A. All shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
B. The 100 surveyed shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
C. All shoppers at the discount store on this particular Saturday.
D. All shoppers at the discount store during a year's time.
E. None of the above.
Answer:
The population is:
D. All shoppers at the discount store during a year's time.
Step-by-step explanation:
Since the discount store wants to determine the average yearly income of its shoppers, the population of interest here is all the shoppers that visit the discount store during a year's time. The population includes all the individual shoppers. However, this number may be too difficult to obtain and work on their data. This is the researcher can choose a sample, calculating its statistics to approximate the population parameters.
Identify the point from the equation y + 5 = 3(x -2)
Which names the function for the following arithmetic series 11,7,3,-1
Answer:
Arithmetic sequence
Step-by-step explanation:
This is an arithmetic sequence, since each new term is obtained by subtracting 4 from the previous term.
Think you can balance this scale?
Yes. balancing an unknown mass against a known mass.
Explanation:Hope it helps
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