Answer:
here you go
Step-by-step explanation:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.
Please help!!
Solve for x
Answer: x=8
Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,
just put 32/40 = 24/3x+6 ,
cross multiply ( 32 x 3x+6 and 40 x 24),
they become 96x +192 = 960.
move 192 to the other side and divide both sides by 96
b. Isabella has a second tray that has a length of 5/3 inches and a width of 13/4 inches
and a height of 5/2 inches. What is the volume of the second tray?
Answer: approx 13.54 (full decimal : 13.416666667)
Step-by-step explanation:
Area = Base Area x Height OR Length x Width x Height
5/3 x 13/4 x 5/2
5 x 13 x 5 = 325
3 x 4 x 2 = 24
325/24 = approx 13.54
The ratio of the sides of a triangle are 3:5:12. If the perimeter of the triangle is 100 units, determine the length of the shortest side.
The measure of the length of the shortest side will be 15 units.
What is a ratio?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.
Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.
The length of the shortest side will be calculated as:-
3x + 5x + 12x = 100
20x = 100
x = 20
Length = 3x
Length = 3 x 5 = 15 units
Hence, the shortest side will be 15 units.
To know more about ratios follow
https://brainly.com/question/18014668
#SPJ9
**EASY POINTS**
2 part question:
1. There is a circular running path in the park. The diameter of the circle is 350 m. What is the length of one lap around the path?
2. Jimmy jogs 3 laps of the circle in question #1 every morning. How long does he jog in 5 days?
Answer:
The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.
Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.
Step-by-step explanation:
pls help asap it’s annoying me
Answer:
b. 53.1°
c. 126.9⁰
Step-by-step explanation:
These are SSA triangles; use Law of Sines to find the unknown angle:
b) sin30/15 = sinA/24
sinA(15) = sin30(24)
sinA = sin30(24)/15 = 0.80
m∠A = sin⁻1(0.80) = 53.1°
c) m∠A = 180 - 53.1 = 126.9⁰
Answer:
∠ BAC = 53.13° , ∠ BAC = 126.87°
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A and c is the side opposite ∠ C
here a = BC = 24 and c = AB = 15 , then
[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )
15 sinA = 24 sin30° ( divide both sides by 15 )
sin A = [tex]\frac{24sin30}{15}[/tex] , then
A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°
(b)
acute angle BAC = 53.13°
(c)
the sine of an angle is positive in both the first and second quadrant , so
obtuse angle BAC = 180° - 53.13° = 126.87°
a department store gets an average of 16 calls in a 2 hour time period. what is the probability that the department store will get at most 3 calls in a 55 minute period? round the final answer to three decimal places.
The probability that the department store will get at most 3 calls in a 55 minute period is 0.066
The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.
It is given that a department store gets an average of 16 calls in a 2 hour or 161055 = 223 calls per minute
Find the probability by Poisson distribution with parameter
λ = 223
P(X = x) = λˣе - λx!
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (223)⁰е - 223(0!) +(223)¹е - 223(1!) +(223)²е - 223(2!) +(223)³е - 223(3!)
= 0.0006 + 0.004 + 0.018 + 0.043
P(X ≤ 3) ≈ 0.066
To know more about Poisson distribution
https://brainly.com/question/24243262
#SPJ4
your friend says that he will be 21 years old and seven years how old is he now?
Answer:
Step-by-step explanation:
He is now 14 years old because if you minus 21 and 7, it will be 14
Answer:
If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.
Step-by-step explanation:
what are the multiplicative inverses of the other elements (you may want to use trial and error for finding the inverses)?
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).
For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:
The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).
The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).
The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).
The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).
The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).
Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.
Learn more about mathematics here: brainly.com/question/24600056
#SPJ4
how many sides does a polygon have if the sum of the interior angles is 3960
A polygon with a sum of interior angles of 3960 has 22 sides.
The sum of the interior angles of a polygon can be calculated using the formula:
(n-2) * 180
where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.
Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.
To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:
n = (Sum of interior angles / 180) + 2
So, if the sum of the interior angles is given as 3960, we can plug that into the formula:
n = (3960 / 180) + 2
n = 22
Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.
To learn more about polygon please click on below link.
https://brainly.com/question/18487663
#SPJ4
How many sides does a polygon have if the sum of the interior angles is 3960?
why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? would the same approach be equally valid for a sample of size 2 rather than 25? why or why not?
In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
The conditions for the CLT are:
The sample is randomly drawn from the population.
The sample size is large (usually, n >= 30 is considered large enough).
The samples are independent.
In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.
Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.
For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.
In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.
In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.
Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.
Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.
(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.
(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?
Learn more about binomial distribution: brainly.com/question/15278907
#SPJ4
amy invested $223 in the banck and a year later has $280,98 . by what percent has changed
David and Alec are comparing the international calling plans on their cell phones. On his plan,
David pays $4 just to place a call and $1 for each minute. When Alec makes an international
call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would
cost exactly the same under both plans. What is the duration?
Write a system of equations, graph them, and type the solution.
3 minutes is the cost of the call that is same for both plans
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's assume the call duration in minutes is represented by x.
For David, the cost of the call can be represented by the equation: C(d) = 4 + x
For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x
Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:
4 + x = 1 + 2x
Solve for x.
3 = x
Hence, the call duration that costs the same on both plans is 3 minutes.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Increase 600 by 9% equal too?
Answer:
654
Step-by-step explanation:
An increase of 9% would mean 1.09 times 600 which equals 654
an advertising company designs a campaign to introduce a new product to a metropolitan area of population 5 million people. let p(t) denote the number of people (in millions) who become aware of the product by time t. suppose that p increases at a rate proportional to the number of people still unaware of the product. the company determines that no one was aware of the product at the beginning of the campaign, and that 10% of the people were aware of the product after 10 days of advertising. the number of people who become aware of the product at time t is:
The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).
The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.
To express the proportionality mathematically, we can use the equation:
p'(t) = k [5 - p(t)]
Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.
To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:
ln|5 - p(t)| = kt + C
Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:
ln|5 - 0| = k(0) + C
Simplifying, we get:
C = ln(5)
Substituting this value into the equation, we get:
ln|5 - p(t)| = kt + ln(5)
To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:
[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]
Simplifying, we get:
[tex]5 - p(t) = 5e^{kt}[/tex]
Or:
[tex]p(t) = 5(1 - e^{kt})[/tex]
To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:
p(10) = 0.1(5) = 0.5
Substituting this into the equation, we get:
[tex]0.5 = 5(1 - e^{10k})[/tex]
Solving for k, we get:
k = -0.1 ln(0.9)
Substituting this value into the equation for p(t), we get:
[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]
Simplifying, we get:
[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
This is the formula that tells us how many people will become aware of the product at time t.
To know more about proportion here.
https://brainly.com/question/30657439
#SPJ4
A pyrotechnician plans for two fireworks
to explode together at the same height In the air. They travel
at
speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after
B Firework B launches will both fireworks explode?
Firework A
Firework B
340 ft/s
260 ft/s
The mentioned scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.
What is the relationship between time, speed and distance ?The distance covered by the object is equal to the product of the speed of object and the time required for it.
Distance = Time x speed
Firework A :
D = 360xt - - - (1)
Firework B:
D = 280x(0.25) + 280xt
D= 70 + 280xt - - - (2)
Equate equation (1) and (2) :
360t = 280t + 70
Collect like terms
360t - 280t = 70
80t = 70
t = 70/80
t = 0.875 seconds
0.875 + 0.25 = 1.125 seconds
Hence, the fireworks will explode after 1.125 seconds of launching Firework B.
To know more about time, speed & distance check: brainly.com/question/7287026
#SPJ9
Julius went fishing on Saturday morning. He took a cooler to store the fish that he caught. The cooler could hold less than 8 large fish. Write an inequality that represents how many fish the cooler could hold.
8 > f
8 < f
8 ≥ f
8 ≤ f
Answer:
8 < f
8 must be strictly lesser than f, not greater than or equals to.
a bin of 50 manufactured parts contains 3 defective parts and 47 nondefective parts. a sample of 6 parts is selected from the 50 parts. write down an expression for the number of different samples of size 6 that contain exactly 2 defective parts.
The expression for the number of different samples is: C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x
(47! / (4! x 43!)).
The number of different samples of size 6 that contain exactly 2 defective parts can be calculated using the binomial coefficient formula:
C(3, 2) x C(47, 4)
where C(n, k) represents the number of ways to choose k objects from a set of n objects.
In this case, we first choose 2 defective parts from the 3 defective parts in the bin, which can be done in C(3, 2) ways. Then we choose 4 nondefective parts from the 47 nondefective parts in
the bin, which can be done in C(47, 4) ways. We multiply these two quantities together to obtain the total number of different samples of size 6 that contain exactly 2 defective parts.
Therefore, the expression for the number of different samples of size 6 that contain exactly 2 defective parts is:
C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x (47! / (4! x 43!))
Learn more about binomial theorem here: brainly.com/question/15368291
#SPJ4
Solve this(the best answer and explanation gets brainliest)
Answer: 5/12
Step-by-step explanation:
- For the ease of the problem, turn them into improper fractions, so it would be:
13/3 divided by 14/5 divided by 26/7
- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:
13/3 times 5/14 times 7/26
- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:
1/3 times 5/2 times 1/2 = 5/12
Answer:
[tex]\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given equation:
[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]
Convert the mixed numbers into improper fractions:
[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]
[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]
[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]
[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]
Multiply the fractions:
[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]
[tex]\dfrac{455}{1092}[/tex]
The greatest common factor of 455 and 1092 is 91.
Therefore, divide the numerator and denominator by the GCF:
[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]
2. Divide R3 520 in the ratio 11:12:17.
Answer:
Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469
Step-by-step explanation:
According to the question, we have to divide rs 3520 in the ratio 11:12:17
let the common ratio be x
so, total share= (11+12+17)x = 40 x
for the first person, share would be (11x/40x)*(Rs 3520)
=Rs 968
for the second person, share would be (12x/40x)*(Rs 3520)
=Rs 1056
for the third person, share would be (17x/40x)*(Rs 3520)
=Rs 1496
The shares are Rs 968, Rs 1056, and Rs 1469
hope this helps :)
Two large charged plates of charge density ±30�C/m2±30μC/m 2 face each other at a separation of 5.0 mm. (a) Find the electric potential everywhere. (b) An electron is released from rest at the negative plate; with what speed will it strike the positive plate?
(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.
What is the word for speed in science?A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.
a). Positivplate should be on the right and negativeplate should be on the left.
Potential equals zero at the center of the plates.
Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0
Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.
Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.
Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.
The potential is -8475 V on the contrary side of the negative plate.
Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.
b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J
Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.
To know more about Speed visit:
https://brainly.com/question/28354412
#SPJ1
4,400 is placed in an account with an annual interest rate of 8. 25%. How much will be in the account after 22 years to the nearest cent
If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08 .
We use the formula for compound interest to find the final amount :
that is ⇒ A = P(1 + r)ˣ ;
where: A = the amount of money in the account after "x years" ;
P(initial amount) = $4400 ; r (interest rate) = 0.0825 ;
⇒ x(time) = 22 years
we get ;
⇒ A = 4400×(1 + 0.0825)²² ;
⇒ A = 4400×(1.0825)²² ;
⇒ A = 4400×6.018028 ;
⇒ A = 26480.08 ;
Therefore , the amount in the account after 22 years is $26480.08 .
Learn more about Interest here
https://brainly.com/question/18446686
#SPJ4
The diameter of a fountain is 9 meters. A sidewalk that is 0.7 meters will be built around it. Find the diameter
Round to the nearest tenth
An estimated Rs. 1863.40 will be needed to cement the route.
What is meant by Cost?A mathematical formula known as a cost function can be used to determine the overall cost of production for a given quantity of goods produced. We'll go into more detail about the cost function below. Representation of unit expenses in relation to the production of 1 or more units during a construction project. For instance, the most popular cost function has the formula y = a + bx, where y is the total cost, an is the total fixed cost, b is the variable cost per unit of production or sales, and x is the number of units produced or sold. This formula sums the fixed costs and the variable costs to represent the total cost.Diameter of park [tex]$=7 \mathrm{~m}$[/tex]
so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]
Width of park [tex]$=0.7 \mathrm{~m}$[/tex]
Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]
Now, Area of path = area of bigger circle -area of smaller circle
[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]
Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]
Cost of Expenditure of cementing the path is Rs. 1863.40.
To learn more about Cost, refer to:
https://brainly.com/question/25109150
#SPJ1
Daniella and her 10 friends are collecting shells on the beach to make crafts. After
they have collected the shells and put them in a pile, they split them evenly among
the group. Each person gets 4 shells. How many shells did they collect as a group?
Select the correct equation and solve for s.
4+ s = 11; s = 7
s/10 = 4; s = 40
4s = 11; s = 2.75
s/11 = 4; s = 44
Daniella and her friends collected a total of 44 shells.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given ,
Daniella and her 10 friends are collecting shells on the beach to make crafts.
After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.
The correct equation for this problem is:
s = 11 x 4
where s is the total number of shells collected.
Simplifying this equation, we have:
s = 44
Therefore, they collected a total of 44 shells.
To learn more about Linear equation from given link.
https://brainly.com/question/13738061
#SPJ1
which statement about 4 √2x+4 √x+3=0 is true?
The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
How to find the equation that is true?To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.
However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.
Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:
(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)
Expanding the left-hand side, we get:
12x + 6 = 0
Solving for x, we get:
x = -1/2
So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
Learn more about equation here:https://brainly.com/question/2972832
#SPJ1
i need help with this one?
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
Find out more on dilation at https://brainly.com/question/11662153
#SPJ1
In August, 18% of the middle school students voted in a school election. The number of students who voted was 213. How many students are in the middle school?
If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .
Let "x" be = total number of middle school students.
We know that 18 percent of the students voted = 0.18x, and is equal to 213 ;
that means , ⇒ 0.18x = 213 ;
Now we need to solve for x,
We divide both sides by 0.18 ;
⇒ x = 213/0.18 ;
Simplifying, we get:
⇒ x = 1183.33
Since the number of students cannot be in decimal ,
So , the actual number of students must be greater than or equal to 1183.33.
Therefore, the middle school has approximately 1184 students.
Learn more about Percent here
https://brainly.com/question/28670903
#SPJ4
Find the value of z such that 0. 14 of the area lies to the left of z. Round your answer to two decimal places.
The value of z is -1.09.
The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given: P(Z<z)=0.14
To find the value of z such that 0.14 of the area lies to the left of z.
We will use z-score table to get the value of z here.
IN z-score table, we have
For P(Z<-1.09)=0.14
Hence, the value of z is -1.09.
Its approximate value is -1.09
So the final answer is z=-1.09.
Know more about Z score click here;
https://brainly.com/question/15016913
#SPJ4
an equation for the line with a slope of 3 and passing through the point (5, 7).
Answer:
y – 7 = 3(x – 5)
Step-by-step explanation:
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]
Use the Distributive Property to figure out (z-5)(z+3)
whats the answer
Using the distributive property, we can write (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
Let us expand the expression (z-5)(z+3).
We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -
(z-5)(z+3) = z(z+3) - 5(z+3)
Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -
z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15
Combining the like terms, we get,
(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15
Therefore, (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
Learn more about the distributive property:
brainly.com/question/28490348
#SPJ4
acrylamide, a possible cancer-causing substance, forms in high-carbohydrate foods cooked at high temperatures. acrylamide levels can vary widely even within the same type of food. an article appearing in a certain journal included the following acrylamide content (in nanograms/gram) for five brands of biscuits. 344 294 333 276 248 (a) calculate the mean acrylamide level (in nanograms/gram). nanograms/gram
An article appearing in a certain journal included the following acrylamide content for five brands of biscuits. 344 , 294, 333, 276, 248. The mean acrylamide level (in nanograms/gram) is 299.
In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. It is commonly referred to as the average.
To calculate the mean, all the data values are added together, and then this sum is divided by the number of data points in the dataset. The formula for calculating the mean is:
mean = (sum of values) / (number of values)
To calculate the mean acrylamide level, we need to add up all the acrylamide levels for the five brands of biscuits and divide the sum by the total number of brands.
Sum of acrylamide levels = 344 + 294 + 333 + 276 + 248 = 1495
Total number of brands = 5
Mean acrylamide level = (Sum of acrylamide levels) / (Total number of brands) = 1495 / 5 = 299
Therefore, the mean acrylamide level is 299 nanograms/gram.
To learn more about mean click on,
https://brainly.com/question/30112112
#SPJ4
