Answer:
z = 1.55
Step-by-step explanation:
The answer is attached.
A pool that is 2.9 m tall cast a shadow that is 1.76 m long. At the Same time, a nearby building casts a shadow that is 38.25m long how tall is the building? round your answer to the nearest meter
Answer:
63m
Step-by-step explanation:
A pool that is 2.9m tall cast a shadow that is 1.76m
At the same time, a nearby building casts a shadow that is 38.25m long.
We are to find the height of the building.
If an object of length 2.9m cast an image of 1.76m ,
Then an image of 38.25m willl be cast by an object of what length?
Cross multiplying this gives:
[tex]\frac{38.25 * 2.9}{1.76}[/tex] = 63.02556818 = 63m (rounded up to nearest meter)
Calculate how much 30% alcohol solution and 80% alcohol solution must be mixed to end up with exactly 14 gallons of a 40% alcohol solution. You'll need ____ gallons of the 80% solution.
Answer:
You'll need 2.8 gallons of the 80% solution.
Step-by-step explanation:
Let the volume of 30% alcohol =x gallons
Then the volume of 80% alcohol =(14-x) gallons
Since we want to obtain a 40% alcohol solution, we have:
0.3x+0.8(14-x)=0.4(14)
0.3x+11.2-0.8x=5.6
0.8x-0.3x=11.2-5.6
0.5x=5.6
x=11.2
Therefore, the volume of 80% alcohol
=14-11.2
=2.8 gallons
You'll need 2.8 gallons of the 80% solution.
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
h
e
l
p
?
p
l
e
a
s
e
To clear the fractions we multiply both sides by the least common multiple of all the denominators.
1/2 x + 2/3 = 4
Denominators 2 and 3, so multiply both sides by [Answer]: 6
3/4 x + 1 = 5/6
Denoms 4 and 6, LCM=12 Answer: 12
6/7 x - 2/3 = 5/21
LCM(7,3,21)=21 Answer: 21
3/5 + x/2 = 9
LCM(5,2) Answer: 10
25/4 = 6 + 1/2 x
LCM(4,2) Answer: 4
Sin?
Cos?
Or Tan???????????????
Answersin -> 48
Step-by-step explanation:
solve for the length of the horizontal line by doing:
sin(55)=x/58
rearrange: x = sin(55) times 58 = 47.51
round UP to 48
Find the inverse of the one-to-one function. F(x) = 7x - 6
Answer:
The inverse is (x+6)/7
Step-by-step explanation:
y = 7x-6
To find the inverse, exchange x and y
x = 7y-6
Solve for y
x+6 = 7y
Divide each side by 7
(x+6)/7 = y
The inverse is (x+6)/7
Find the volume of the solid that is generated when the given region is revolved as described. The region bounded by f(x)equalse Superscript negative x, xequalsln 16, and the coordinate axes is revolved around the y-axis.
Answer:
The answer is "[tex]= \frac{\pi}{8}(15-41n^2 )\\[/tex]".
Step-by-step explanation:
The radius = x
the value of height is= [tex]e^{-x}[/tex]
The Formula for the volume by the shell method:
[tex]\bold{V= \int\limits^b_a {(2\pi\ rad)(height)} \, dx }[/tex]
[tex]= 2\pi \int\limits^{In 16}_0 {xe^{-x}} \, dx\\\\\\= 2\pi {(e^{-x}[-x-1])}_{0}^{In 16}\\\\ = 2\pi {(\frac{1}{16} \times (15-41n^2 ))}\\\\ = \frac{\pi}{8}(15-41n^2 )\\[/tex]
What is the vertex of this parabola y=-5x^2-10x-13
Step-by-step explanation:
Vertex for your equation is (-1, -8)
Mikayla asked 10 of her friends how many hours of TV they watch in a week. Three of her friends said 8 hours, two of
her friends said 9 hours, two of her friends said 11 hours, one of her friends said 12 hours, and two of her friends said
14 hours. Mikayla wanted to make a dot plot of the data she gathered. In what order would she create the dot plot?
Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.
Show the frequency of each number. Title the dot plot. Draw a number line from 8 to 14.
Title the dot plot. Show the frequency of each number. Draw a number line from 8 to 14.
<-------------------------------------------------->
8 9 10 11 12 13 14 (number of hours spent)
dot plot
Answer:
(A) Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.
Step-by-step explanation:
a man is 3 times as old as his son . the sum of their ages is 48 years .how old is the son ? how old is the dad?
Answer:
son is 12
dad is 36
Step-by-step explanation:
Say the son is x years old.
Then the father is 3x. Also 3x+x must be 48.
So 4x = 48 => x= 48/4 = 12
Let x be how old the son is. We know that the dad is 3 times older and their sum is 48. Creating an equation to represent this situation gives us:
[tex]x+3x=48[/tex]
[tex]4x=48[/tex]
Divide both sides by 4
[tex]x=12[/tex]
The son is 12 years old, but we want to find the age of the dad. Since we know the dad is 3 times older, multiply 12 with 3
[tex]12 \times 3 = 36[/tex]
The dad is 36 years old. Let me know if you need any clarifications, thanks!
Help pls!!!!!!!!!!!!!!!!!!!!!!!!!!♥️
Answer:
A
Step-by-step explanation:
when using the rational root theorem, which of the following is a possible root of the polynomial function below f(x)=x^3-5x^2-12x+14
A.9
B.3
C.7
D.5
Answer:
[tex]\Large \boxed{\sf \ \ 7 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The polynomial function is
[tex]x^3-5x^2-12x+14[/tex]
The rational root theorem states that each rational solution
[tex]x=\dfrac{p}{q}[/tex]
, written in irreducible fraction, satisfies the two following:
p is a factor of the constant term
q is a factor of the leading coefficient
In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.
Let's proceed with the prime factorisation of 14:
14 = 2 * 7
Finally, the possible rational roots of this expression are :
1
2
7
14
and we need to test for negative ones too
-1
-2
-7
-14
From your list, the correct answer is 7.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
the answer is C.) 7
Convert the measurement. Use unit fractions or the metric conv
38 L to mL
38 L =
mL. (Type a whole number or a decimal.)
A car started from town p and travelled towards town Q at 70 km/h. at the same time a van started from town Q and travelled to town p at 60km/h after 11/4 hours they were 65 km apart ,still travelling toward each other
Answer:
422.5km
Step-by-step explanation:
Car A started from point P to point R in 11/4hrs by the speed of 70km/hr
Distance = speed × time
= 70×11/4
= 770/4
= 192.5km
Car B
Started from point R and headed to point S in 11/4 hrs by speed of 60km/hr
Distance travelled = speed × time
= 60× 11/4
= 660/4
= 165km
Distance travelled from P to Q
= PR+RS+SQ
= 192.5+65+165
= 422.5km
Please answer this correctly without making mistakes Please simplify the correct answer
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
There are 6 brooms and 4 mops in a janitor's closet. What is the fraction of the number of brooms to the number of mops?
Answer:
6/4
Step-by-step explanation:
Answer:
6/4
Step-by-step explanation:
There are 6 brooms to 4 mops.
So you would write it that way as a fraction, but you could also write it like 6:4 or 6 to 4.
Urelia made a deposit to her checking account. She had $104.00 in currency; $7.64 in coins; and checks for $83.29, $257.77, $1,332.68, and $3,984.05. What was her total deposit?
Which of the following is a rational function?
F(x)=8x^2-21x+45
F(x)= 3 root of X +17
F(x)= 16x
F(x)= 5x/x^2-25
What is heron's formula
Answer:
[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
Step-by-step explanation:
We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s : \mathrm{semi \: perimeter}[/tex]
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]A : \mathrm{area}[/tex]
Answer:
Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.
Step-by-step explanation:
A researcher wants to study the relationship between salary and gender. She randomly selects 297 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?
Answer:
The researcher cannot conclude that salary and gender are dependent.
Step-by-step explanation:
A dependent variable is a variable, for example "Salary" that depends on an independent variable, e.g. "Gender." Salary is the dependent variable while gender is the independent variable. This means that the value of salary changes in relation to the gender and not vice versa. Two variables become dependent if they change based on another independent variable that is operating on them. In this research, the researcher is not trying to measure gender but the relationship between salary and gender. To achieve her purpose, she shows that salary depends on gender and not that gender depends on salary.
Help ASAP
Picking the first second and third place winners at a track meet is an independent event.
False
Or
True
false, an independent event is an event that isn't affected
The statement given is false
What is a dependent event?
Two events are dependent, when the outcome of the first event influences the outcome of the second event.
Given that, Picking the first second and third place winners at a track meet is an independent even,
This statement is not correct.
The event is a dependant variable, the 1st person is picked based on the 1st mark on the track, so is the second and the 3rd. their position influence the outcome of the other.
the position of the 1st, 2nd or 3rd is influenced by time and speed, so the positions will be picked based on the participant scores /effect of time or speed of the 1st person to reach the track meet.
For more references on dependent events, click;
https://brainly.com/question/12138721
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Cell phone bills for residents of have a mean of $47/line with a standard deviation of $9/line. Find the probability that the average cost/line for the Math
What is the area of the shaded region? 21 mm2 24 mm2 42 mm2 48 mm2
Answer:
B or 24 mm2
Step-by-step explanation:
Just did the test :)
The area of the shaded region is 24mm^2
What is the area of triangle?Let b be the base and h be the height of the triangle. The area of the triangle is given by bh/2 square units.Step 1: Find area of the larger triangle
Here base b = 5 mm
Height h = 12 mm
Area of the larger triangle = (5*12)/2 = 60/2 = 30mm^2
Step 2: Find area of the smaller triangle
Here base b = 3 mm
Height h = 4 mm
Area of the smaller triangle = (3*4)/2 = 12/2 = 6 mm^2
Step 3: Find area of the required shaded region
Area of the required shaded region = Area of larger triangle - Area of smaller triangle
= 30 mm^2 - 6 mm^2
=24 mm^2
Hence, the area of the shaded region is 24mm^2
Learn more about area of triangle here:
https://brainly.com/question/17335144
#SPJ2
Solve: 0.1m−1.3m=−2.1−2.7.
Answer:4
Step-by-step explanation:
Simplify what you can which is 0.1m-1.3m
you end up getting -1.2m
Now do the other side of the equation which is 2.1-2.7 which is -4.8
Divide -4.8 by -1.2 to get m=4
Answer: m=4
Step-by-step explanation:
[tex]0.1m-1.3m=-2.1-2.7[/tex]
add like terms
[tex]-1.2m=-2.1-2.7[/tex]
subtract
[tex]-2.1-2.7=-4.8[/tex]
[tex]-1.2m=-4.8[/tex]
multiply both sides by 10
[tex]-12m=-48[/tex]
divide -12 on both sides
m=4
Sum of two consecutive integers is -221
Answer:
-111 and -110
Step-by-step explanation:
If x is the lesser integer, and x+1 is the next integer, then:
x + x+1 = -221
2x = -222
x = -111
x+1 = -110
The two integers are -111 and -110.
Answer:
-111,-110
Step-by-step explanation:
Let n represent the first integer. Then n+1 will represent the next consecutive integer.
Translate into an equation.
We can restate the given information in one sentence as "The sum of the integers is −221."
As an equation this sentence is represented as:
n+n+1=−221
Solve the equation.
n+n+1=-221
2n+1=−221
2n=−222
n=−111
So, n=−111 is the first integer and n+1=−110 is the second integer.
The contingency table represents a box of cards. Box of Cards 1 2 3 4 5 Total Black 1 1 1 1 1 5 Red 1 1 1 0 0 3 Total 2 2 2 1 1 8 What is the probability that a card chosen at random is black and 1?
Answer:
[tex]Probability = \frac{1}{8}[/tex]
Step-by-step explanation:
Given
Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total
Black --------------1 ---1 ----1 ----1 ---1 ----5
Red ---------------- 1 ---1 ----1 ----0--- 0--- 3
Total --------------- 2 ---2 --2-----1 -----1 ---8
Required
Determine the probability of a card being black and being card 1
To solve this, we the the number of card 1 that is black
This is shown below
Box of Cards -- 1
Black --------------1
This implies that, 1 card is black and also card 1
Represent this with [tex]n(Black\ and\ 1)[/tex]
[tex]n(Black\ and\ 1) = 1[/tex]
Next, is to get the total number of cards
From the given parameters;
[tex]Total = 8[/tex]
The probability is calculated as follows
[tex]Probability = \frac{n(Black\ and\ 1)}{Total}[/tex]
[tex]Probability = \frac{1}{8}[/tex]
3 sides of the triangle are distinct perfect squares. What is the smallest possible perimeter of the triangle?
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
Answer:
e
Step-by-step explanation:
e
The length of time, in hours, it takes a group of people, 40 years and older, to play one soccer match is normally distributed with a mean of 2 hours and a standard deviation of 0.5 hours. A sample of size 50 is drawn randomly from the population. Find the probability that the sample mean is less than 2.3 hours. g
Answer:
[tex]P(\overline X < 2.3) = 0.9999[/tex]
Step-by-step explanation:
Given that:
mean = 2
standard deviation = 0.5
sample size = 50
The probability that the sample mean is less than 2.3 hours is :
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{2.3 - 2.0}{\dfrac{0.5}{\sqrt{50}}})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{0.3}{0.07071})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq 4.24268)[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq 4.24)[/tex]
From z tables;
[tex]P(\overline X < 2.3) = 0.9999[/tex]
HELP! WILL GIVE BRAINLIEST!
Answer:
Her eye discourses; I will answer it.
I am too bold; ’tis not to me she speaks:
Two of the fairest stars in all the heaven,
Having some business, do entreat her eyes
To twinkle in their spheres till they return.
Step-by-step explanation:
Write as an algebraic expression and simplify if possible:
A number that is 20% greater than b
Answer:
1.2b
Step-by-step explanation:
When we say, "a number that is 20% greater than b," we're talking about a number that is ...
b + 20%×b
= b + 0.20b
= b(1 + 0.20)
= 1.2b