Answer:
-3 1/2 or -3.5
Step-by-step explanation:
* means multiply
just put 3 where the x is
so
f(x) = -2 ( 1 - 1/4 x )
f( -3) = -2 ( 1 - 1/4 * -3 )
f( -3) = -2 ( 1 3/4 )
f( -3) = - 3 1/2
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. What is the probability that fewer than 11 of them will vote
Answer:
0.0479 = 4.79% probability that fewer than 11 of them will vote
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of all eligible voters will vote in the next presidential election.
This means that [tex]p = 0.7[/tex]
20 eligible voters were randomly selected from the population of all eligible voters.
This means that [tex]n = 20[/tex]
What is the probability that fewer than 11 of them will vote?
This is:
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]
[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]
[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]
[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]
[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]
[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]
The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]
0.0479 = 4.79% probability that fewer than 11 of them will vote
5338 wins in 34 years
Answer:
is that a question?????????????
Define the word term
Answer:
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.
hope this helps
have a good day :)
Step-by-step explanation:
The subjects of an experiment should be selected at random so that they
represent the population from which they come.
O
A. True
O
B. False
Answer: True
Step-by-step explanation:
The subjects of an experiment should be selected at random so that they
represent the population is true.
Once the sample size has been decided, a sample should be taken from the sample size which will represent the population. This gives everyone an equal chance of being selected as there's no bias.
Use logarithmic differentiation to differentiate the question below
[tex]y = x \sqrt[3]{1 + {x}^{2} } [/tex]
Answer:
[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Step-by-step explanation:
[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
PRE-ACTIVITIES/PRE-TEST
5. A tyF
ASK #1
Directions: Draw a star (★) if the statement
lescribes the effects of typhoons and a circle (•) if it is not. Write your answers
1 your notebook.
a. less
b.fror
c.gre
d.gr
(P
th
U
1. The farmers' crops are destroyed when there are heavy rains which
result to flooding.
2. Loss of lives and damage to properties happen due to fiooding and
landslides
3. Thousands of families become homeless.
4. Fishermen can go fishing and abundant catch awaits them.
5. The power supply is cut off for several days as falling trees destroy the
electric posts and power lines.
6. People lose their homes and means of livelihood.
7. The prices of basic commodities become cheaper.
8. People visit malls for shopping.
9. A few houses of first-class materials are partially damaged,
10. Children play on the playground.
Answer:
Step-by-step explanation:
★1. The farmers' crops are destroyed when there are heavy rains which
result to flooding.
★2. Loss of lives and damage to properties happen due to fiooding and
landslides
★3. Thousands of families become homeless.
•4. Fishermen can go fishing and abundant catch awaits them.
★5. The power supply is cut off for several days as falling trees destroy the
electric posts and power lines.
★6. People lose their homes and means of livelihood.
•7. The prices of basic commodities become cheaper.
•8. People visit malls for shopping.
•9. A few houses of first-class materials are partially damaged,
•10. Children play on the playground.
2 times the sum of a number and 9 equals 4
Answer
Step-by-step explanation:
Please help!! This is timed!!
Find the value of x
A. 20
B. 28
C. 10
D. 50/7
Answer:
x=28
Step-by-step explanation:
Step 1, comparing triangles:
Let us look at [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].
They both share [tex]\angle A[/tex] ([tex]\angle A=\angle A[/tex])[tex]\angle ABC = \angle BDE[/tex] (Corresponding Angle Theorem)[tex]\angle ACB = \angle CED[/tex] (Corresponding Angle Theorem)Therefore, because of AAA (Angle Angle Angle), [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] are similar.
Step 2:
Because the two triangles are similar, their sides should be proportional. Notice that [tex]\overline{AB}[/tex] and [tex]\overline {AD}[/tex] should be proportional.
Therefore, [tex]\overline{AB}[/tex]: [tex]\overline {AD}[/tex] =
[tex]12:30+12=\\12:42=\\2:7[/tex]
(Note, [tex]\overline {AD}[/tex] = [tex]\overline{AB}[/tex]+ [tex]\overline{BD}[/tex]=12+30)
Step 3:
We figured out that [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] have proportional sides of 2:7. Therefore, [tex]\overline{BC}[/tex] and [tex]\overline{DE}[/tex] should also have a ratio of 2:7.
[tex]8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}[/tex]
x=28
I hope this helps! Let me know if you have any questions :)
Answer:
x = 20
Step-by-step explanation:
If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.
AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...
x = 2.5(BC)
x = 2.5(8)
x = 20
Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?
Step-by-step explanation:
[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3
(⅛ + ¾ +1)n = 48.75
15/8 n = 48.75
1.875 n = 48.75
n = 48.75/1.875
n = 26
so, the cost of :
the brush = ⅛×26 = $ 3.25
the sketchbook = ¾×26 = $ 19.5
the pain set = $ 26
I can't find the surface area lol
n=3.14
Answer:
216 square feet
Step-by-step explanation:
The formula for the surface area of a rectangular prism is:
2 (lw + hl + hw)
w= width
h= height
l= length
Use the formula with the given dimensions:
2 (6 • 2 + 12 • 6 + 12 • 2)
= 2 (12 + 72 + 24)
= 2 (108)
= 216
Surface area is measured in square feet
(feet in this case)
Hope this helps
determine the value of a in the figure shown
Answer:
d
Step-by-step explanation:
180-149= 31.
31+ 122= 153
180-153= 27
a= 27
In circle Q, the mLKM is 255º. Find the measurement of
Hope this help!!!
Have a nice day!!!
A 25 foot ladder is leaning against a tree. If the base of the ladder is 6 feet
away from the base of the tree, how high, to the nearest tenth, does the
ladder reach up the tree?
9514 1404 393
Answer:
24.3 ft
Step-by-step explanation:
If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...
h² +6² = 25²
h² = 625 -36 = 589
h = √589 ≈ 24.3
The ladder reaches about 24.3 feet up the tree.
if 4 labourers can finish a job in 6days how long would it take 3men to do the job
Answer:
yes do have in an any job that occurred the an evrey one to know you.
Answer:
8 days
Step-by-step explanation:
no of men no of days
4 6
3 let be x
there is indirect variation
4/3=6/x
since it is in indirect variation do the reciprocal of any one fraction among these two fractions
4/3=x/6
do cross multiplicatin
3*x=6*4
x=24/3
x=8
therefore it take 8 days to complete the same work by 3 men.
please help! (listing BRAINLIST and giving points) :D
Answer:
40°
Step-by-step explanation:
because angle In an isosceles triangle base angles are same and angle in a triangle add up to 180° and angle on a straight line add up to 180°
hope this helps:)
The volume of a particular die is 6000 mm. Use the fact that 10 mm equals 1 cm to convert this
volume to cm.
Answer:
600 cm³
Step-by-step explanation:
6000 mm/10 mm = 600 cm
PLEASE HELP I WILL GIVE BRAINLIEST TO THE FIRST PERSON THAT ANSWER PLEASE
Answer:
[tex]a) x = k \times \frac{1}{y^2} \ , \ where \ k \ is \ a \ constant\\\\b) x = 3, \ when\ y\ =\ 10\\\\c) y = 10, \ when \ x = 3[/tex]
Step-by-step explanation:
a)
[tex]x \ \alpha \ \frac{1}{y^2}\\\\x = k \times \frac{1}{y^2}\\\\[/tex] [tex][ \ where \ k \ is \ a \ constant \ ][/tex]
Find k.
Given x = 12, y = 5,
[tex]12 = k \times \frac{1}{5^2}\\\\k = 12 \times 25 = 300[/tex]
b)
Find x.
Given y = 10
We have k = 300
[tex]x = k \times \frac{1}{y^2}\\x = 300 \times \frac{1}{10^2} \\\\x= \frac{300}{100} = 3[/tex]
c)
Find y
Given x = 3
We have k = 300
[tex]x = k \times \frac{1}{y^2}\\\\3 = 300 \times \frac{1}{y^2}\\\\\frac{1}{y^2} = \frac{3}{300}\\\\\frac{1}{y^2} = \frac{1}{100}\\\\y^2 = 100\\\\y = \sqrt{100} = 10[/tex]
A factory manufactures motorcycles. One of its employees, working in the quality control department, checks the first 10 and the last 10 motorcycles manufactured in a day. This is what type of sampling?
Answer:
Convenience sampling
Step-by-step explanation:
When sampling is done based in degree of ease or samples picked from observations that are easily accessible rather than prioritizing randomness or selection which will most be representative of the population, then such sampling is called convenience sampling. In some texts, it is also referred to as grab sampling as researchers choose from close, easy to reach samples. In the scenario above, the quality control takes the easy procedure of checking the first and last 10 motorcycles as this is easier than having to take samples at random tune intervals which will be a better representation of the entire motorcycles.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
Answer:
Average rate of change = 5
Step-by-step explanation:
Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,
Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]
From the table,
f(5) = 10
f(4) = 5
Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]
= 5
Answer:
=5
Step-by-step explanation:
I’ll need brainliest
Answer:
I think no B
if wrong correct me pls
I HOPE IT HELPS
HAVE A GREAT DAY
[tex]#Liliflim[/tex]
Answer:
B
Step-by-step explanation:
C=7s
Triangle ABC is similar to triangle EFD what scale factor is required to dilate triangle abc so that it's image, ABC is congruent to triangle EFD
Step-by-step explanation:
the scale factor k = 5/12
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
From the figure attached, we are given that Triangle ABC is similar to triangle EFD.
Therefore,
BC/ FD = AC/ ED
These corresponding sides are proportional.
Scale factor;
EF / AB = 5/12
Then Angle between this sides is also equal.
The SAS rule of similarity of triangles states that two triangles will be similar if their corresponding two sides are proportional and the angle between these two sides is equal.
The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.
Learn more about scale factors here:
https://brainly.com/question/11178083
#SPJ2
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval
Did you manage to solve it?
If x = -3 and y = 4x - 1, then y equals what number
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{y = 4x - 1}[/tex]
[tex]\large\text{If x= -3, then substitute it into the given equation}[/tex]
[tex]\large\textsf{y = 4(-3) - 1}[/tex]
[tex]\large\textsf{4(-3) = \boxed{\bf -12}}[/tex]
[tex]\large\textsf{y = -12 - 1}[/tex]
[tex]\large\textsf{-12 - 1 = y}[/tex]
[tex]\large\textsf{-12 - 1 = \boxed{\bf -13}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf y = -13}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex] \quad \quad \quad \quad\tt{y = 4x - 1}[/tex]
[tex] \quad \quad \quad \quad\tt{y = 4( - 3) - 1}[/tex]
[tex] \quad \quad \quad \quad\tt{y = (- 12)- 1}[/tex]
[tex] \quad \quad \quad \quad\tt{y = - 13}[/tex]
Hence, The value of y is:[tex] \quad \quad \quad \quad \boxed{\tt \color{green}{y = - 13}}[/tex]
______
#LetsStudy
There are 2 people in the Hill family. Each person
reads the same number of books. They read 12 books
in all. How many books does each person read?
A
18 books
B
6 books
C
8 books
D
10 books
Answer:
6
Step-by-step explanation:
When 390 junior college students were surveyed,115 said that they have previously owned a motorcycle. Find a point estimate for p, the population proportion of students who have previously owned a motorcycle.
a. 0.705
b. 0.228
c. 0.295
d. 0.418
Answer:
0.2948 ≅ 0.295
Step-by-step explanation:
According to the Question,
Given, 390 junior college students were surveyed,115 said that they have previously owned a motorcycle .So, the population proportion of students who have previously owned a motorcycle is 115/390 ⇔ 0.2948 ≅ 0.295
Which of the following rational functions is graphed below?
A. F(x) =1/(x-4)^2
B. F(X) =1/(x + 4)^2
C. F(X) = 1/4x^2
D. F(x) = 4/x^2
Answer to your question is B. f(x)= 1/(x+4)^2
The equation of the rational function is f(x) = 1/(x + 4)^2
How to determine the graph?From the figure, we have the following property:
Vertical asymptote at;
x = -4
Add 4 to both sides
x + 4 = 0
Square both sides
(x + 4)^2 = 0
The above means that the denominator of the equation of the graph is (x + 4)^2
So, we have:
f(x) = 1/(x + 4)^2
Hence, the equation of the rational function is f(x) = 1/(x + 4)^2
Read more about rational function at:
https://brainly.com/question/1851758
#SPJ6
Which drink has more sugar per fluid ounce? 50 POINTS
Negative six multiplied by negative ten is subtracted from eight multiplied by five. Find the number
Answer:
The answer is -20.
Step-by-step explanation:
(8 × 5) - (-6 × -10)
= 40 - 60
= -20
Pythagorean theorem.
I hope this is help full to you
Answer:
3
Step-by-step explanation:
because this is the formula of Pythagorean theorem a^2 + b^2 = c^2 so all I did was 5^2 = 25 - 4^2 = 25-16 = 9 and square root of 9 = 3 i hope this helps. :D please give brainliest
