Answer:
[tex]\frac{2\sqrt3}{3} = x[/tex]
Step-by-step explanation:
So you want to use PEMDAS to do the equation in order. This means that you'll start by adding 6 and 1 and then multiplying that value by 2
[tex]2(7)-|-10| = 3x^2[/tex]
[tex]14-|-10|=3x^2[/tex]
The absolute value can be defined as the "distance" from 0 which is going to be positive. You can think of it as the positive value of a number so if you have |-b| it will become b, and even if it's already positive, it will remain positive. so the absolute value of -10 is 10 but then it becomes negative again because of the subtraction
[tex]14-10=3x^2[/tex]
[tex]4=3x^2[/tex]
Now you want to solve for x by dividing both sides by 3 and taking the square root of both sides to isolate x
[tex]\frac{4}{3} = x^2[/tex]
[tex]\sqrt{\frac{4}{3}}=x[/tex]
You can distribute the square root across division since [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] and the square root can be defined as [tex]x^{0.5}[/tex] since [tex]a^b * a^c = a^{b+c}[/tex] because if you spread it out it's really just [tex](a * a * a ... b\ amount \ of \ times) * (a * a * a ... c\ amount\ of\ times)[/tex] which can be simplified to (a * a * a... (b + c) amount of times) if that makes any sense. Anyways using this property you'll get [tex]a^{0.50} * a^{0.50} = a^{0.50 + 0.50} = a^1 = a[/tex]. If you look at it you'll notice a^0.50 multiplied by it self gives you a... sounds like the square root, which it is. So now the equation becomes
[tex]\frac{\sqrt{4}}{\sqrt{3}}=x[/tex]
[tex]\frac{2}{\sqrt3}[/tex]
Now if you look at the equation you'll notice there's a radical in the denominator, which can be rationalized by multiplying by sqrt(3)\sqrt(3) which is 1 except it makes the denominator 3 and keeps the original value
[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3}=x\\\frac{2\sqrt{3}}{3} = x[/tex]
Pls help! Geometry
What is the area of the square?
Area of the circle?
Area of the blue section?
(a) By the formula for the area of a square, the answer is [tex]16^2 = 256[/tex] square km
(b) By the formula for the area of a circle, the answer is [tex](\pi)\left(\frac{16}{2} \right)^2 =64\pi[/tex] square km
(c) Subtracting areas, we get [tex]256-64\pi[/tex] square km
HELPPP PLS TYSM IF U HELPED <3
The measure of <TRS and angle d are 70 and 43degrees respectively
Triangles and angleThe given triangles are isosceles triangles since they have two equal sides.
14) From he triangle RST
<TRS + 90 + 20 = 180
<TRS + 110. = 180
Subtract 110 from both sides
<TRS = 180 -110
<TRS = 70 degrees
15) For this triangle;
d = 86/2
d = 43 degrees
Hence the measure of <TRS and angle d are 70 and 43degrees respectively
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A student hypothesized that in the US adult population, women drank the same amount of water per day as men per kg of body weight as the null hypothesis. The probability value for her null hypothesis was 0.02. Assume the alpha level was 0.05. Which conclusion is justified?
The conclusion that is justified based on the research is that he rejected the null hypothesis that women drank the same amount of water per kg of body weight per day as men.
How to illustrate the research?It should be noted that a research is simply used to get information about a topic.
In this case, it can be deduced that a type 1 error is committed. This implies the rejection of the null hypothesis when it's true.
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Find a polynomial function of degree 5 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 3 as a zero of multiplicity 1.
[tex](x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x[/tex]
whats the rule (-2,-7) (0,-1) (7, 22)
The rule of the points is y = 3.2x - 0.7
How to determine the rule?The points are given as:
(-2,-7) (0,-1) (7, 22)
The above points form an approximate linear equation.
So, we make use of a linear regression to determine the rule
When the above points are entered in a statistical calculator, we have the following summary:
Sum of X = 5Sum of Y = 14Mean X = 1.6667Mean Y = 4.6667Sum of squares (SSX) = 44.6667Sum of products (SP) = 144.6667The regression equation is then represented as:
y = bx + a
Where
b = SP/SSX = 144.67/44.67 = 3.23881
a = MY - bMX = 4.67 - (3.24*1.67) = -0.73134
This gives
y = 3.23881x - 0.73134
Approximate
y = 3.2x - 0.7
Hence, the rule of the points is y = 3.2x - 0.7
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You obtain a 60-day note from a bank for $5200. The loan takes place on November 20, and the costs include $73.38 for interest and $29.12 in other charges. How much, in dollars, is due at the end of 60 days?
Answer:=102.5
Step-by-step explanation:
A family has to travel 380 miles to reach their vacation spot. They plan to stop for lunch after driving 2/5 of the distance. How far will they have traveled when they stop for lunch?
Answer:
152 miles
Step-by-step explanation:
380/5 = 76
76*2 = 152
as they will have traveled 2/5, you would need to divide your miles by 5 then multiply by 2!
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.Find the probability that the person has an IQ score between 92 and 108.
Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex].
The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:
X = 108:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{108 - 100}{15}[/tex]
Z = 0.53
Z = 0.53 has a p-value of 0.7019.
X = 92:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 100}{15}[/tex]
Z = -0.53
Z = -0.53 has a p-value of 0.2981.
0.7019 - 0.2981 = 0.4038.
0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
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Match each problem to its solution 8,8.2,9,56.25
The computation shows that the amount will be:
$56.25.$988.2 poundsHow to compute the values?Jonah earns $12.50 per hour
He works for 4.5 hours
Amount he earned will be:
= 12.50 × 4.5 = $55.25
Items worth is $41.23
Amount paid is $50.23
Extra amount paid will be:
= 50.23 - 41.23
= $9
Length of cloth available is 20 m
Length of one long-sleeved blouse is 2.5m
Number of blouses that can be made will be:
= 20/2.5 = 8
Potatoes weight is 3.2 pounds
Oranges weight is 2.3 pounds
Onions weight is 2.7 pounds
Total weight of the purchase will be:
= 3.2 + 2.3 + 2.7 = 8.2 pounds
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Complete question:
Match each problem to its solution. 8 8.2 9 56.25 Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn? arrowRight Jessica purchased items worth $41.23 at the local grocery store. The cashier made a mistake while ringing up her items, and Jessica ended up paying $50.23. How many extra dollars did she pay? arrowRight Josie has 20 meters of cloth. She needs to make long-sleeved blouses with that cloth. If one long-sleeved blouse requires 2.5 meters of cloth, how many blouses can she make with the material? arrowRight Jeremy bought 3.2 pounds of potatoes, 2.3 pounds of oranges, and 2.7 pounds of onions. How many pounds does his purchase weigh? arrowRight
How many solutions exist for the system of equations in the graph?
Answer:
Two
Step-by-step explanation:
Solutions are when the two graphs intersect
f(x)=(2x−1)(3x+5)(x+1) has zeros at x= -5/3, x= -1 and x= 1/2 What is the sign of f on the interval -5/3
The sign of f on the interval -5/3 is negative
How to determine the sign?The function is given as:
f(x)=(2x−1)(3x+5)(x+1)
The zeros of the function are
x= -5/3, x= -1 and x= 1/2
Next, we plot the graph of the function
At x = -5/3, the function approaches negative infinity
This means that the sign of f on the interval -5/3 is negative
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pleasee help!!!!
20 points
The function with the same end behavior of f(x) is the last option:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Which function has the same end behavior of f(x)?
By looking at the graph, we can see that the end behavior of f(x) is:
as x → ∞; f(x) → -∞
as x → -∞; f(x) → ∞
Then we just want a function that depends linearly with x and that has a negative coefficient.
The correct option is the last one:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Where clearly, when x tends to infinity the function tends to negative infinity, and when x tends to negative infinity, the function tends to infinity.
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Juanita has 60 horses on her ranch. If 60% of the horses are thoroughbreds, how many are not thoroughbreds?
A.) 45
B.) 22
C.) 21
D.) 24
Answer: d
Step-by-step explanation:
60*0.6=36
60-36=24
24 are not thoroughbreds
Select the equation of the line that passes through the point (–2, 1) and has slope 3 in point-slope form.
(x – 2) = 3(y + 1)
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Select the equation that passes through (-2,1) and has slope 3
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula used, here [tex]\bf{y-y1=m(x-x1)}[/tex]
[tex]\bf{y-1=3(x-(-2)}[/tex] | put in the values, then, simplify
[tex]\bf{y-1=3(x+2)}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y-1=3(x+2)}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]
∞
A sample of 4 different calculators is randomly selected from a group containing 12 that are defective and 33 that have no defects. What is the probability that at least one of the calculators is defective?
The probability that at least one of the calculators is defective is : 0.725
What is probability?Probability is the likelihood of an event happening or not.
if there is certainty that the event would happen probability is 1.
Analysis:
probability = required outcome/possible outcome
for 33 good calculators and 12 defective calculators, total calculators = 45
4 calculators were chosen, possible outcome = 45C4 = 148995
Required outcome = 33C3 . 12C1 + 33C2 . 12C2 + 33C1 . 12C3 + 33C0 . 12C4
= 65472 + 34848 + 7260 + 495 = 108075
Probability = 108075/148995 = 0.725
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On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform B and zip to the other platform. What is the coordinate when you reach half way?
what is the midpoint
The distance from Platform B to Platform C is 26.926 units
The given parameters are;
The zip-line course distance from platform A to platform F is given;
On the given graph of the path of travel we have;
Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5).
What is the distance formula?
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula
[tex]l=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)
Which gives
[tex]l=\sqrt{(5-(-20))^2}+((-15)-(-25))^2\\l=26.926 units[/tex]
The distance from points B to C = 26.926 units. The distance from Platform B to Platform C is 26.926 units.
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The Jones family bought a refrigerator for $900. They paid installments over 4 years at an add-on rate of 6%. What is the approximate APR? ASAP
The approximate APR for the purchase is 16%
To calculate the annual percentage rate (APR)
We would calculate the interest rate
Add the administrative fees to the interest amount
Divide the loan amount (principal)
Divide by the total number of days in the loan term
Multiply all year
Multiply by 100 to convert to a percentage
Interest= P * R * t
APR= [tex]\frac{\frac{216}{900}}{6 * 4 * 100}[/tex]
APR = 16%
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which of the fallowing is a mononial
Answer:
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.
Which inequalities would have a closed circle when graphed? check all that apply. x > 2.3 5.7 less-than-or-equal-to p one-half greater-than y m greater-than-or-equal-to 10 s < –7.6
Option B and D would have closed circles when graphed
The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.
At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.
∴ Option B and D that are 5.7 ≤ p and [tex]\frac{1}{2}[/tex] ≥ y respectively would have closed circles
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find the area of a triangle whose sides are 5 m, 6 m and 9m,( use root 2 =-1.41 m)
The area of the triangle is 14.1 square meters
How to determine the triangle area?The side lengths are given as:
5m, 6m and 9m
Calculate the semi-perimeter (s) using
s = (5 + 6 + 9)/2
Evaluate
s = 10
The area is then calculated as:
[tex]Area = \sqrt{s(s -a)(s-b)(s-c)[/tex]
This gives
[tex]Area = \sqrt{10 * (10 -5)(10-6)(10-9)[/tex]
Evaluate the products
[tex]Area = \sqrt{200[/tex]
Evaluate the exponent
Area = 14.1
Hence, the area of the triangle is 14.1 square meters
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Which of the following is equivalent to 6^2/5
Where are the options?
A ______ of two linear _______ can have one solution, an infinite number of solutions, or no solution.
Answer:
system
equations
Step-by-step explanation:
Answer:
A system of two linear equations can have one solution, an infinite number of solutions, or no solution.
===================================================
Explanation:
An equation is something like [tex]\text{y} = 2\text{x}+5[/tex] and [tex]\text{y} = 3\text{x}+7[/tex]
When we combine two such equations to form a group (of sorts), we consider this to be a system of equations.
We use a single curly brace to write the system
[tex]\begin{cases}\text{y} = 2\text{x}+5\\\text{y} = 3\text{x}+7\end{cases}[/tex]
Here are the three cases mentioned when it comes to solutions.
If the two lines intersect at exactly one point, then the system has exactly one solution. This system is consistent and independent.If the two lines are the same, they intersect at infinitely many points along that line. One line perfectly overlaps the other. Therefore, this scenario leads to infinitely many solutions. The system is dependent because one line depends on the other (since they are one in the same). This system is also consistent because it has at least one solution. Lastly, if the two lines are parallel, then they never cross. The lack of crossing points means there aren't any solutions. We call this an inconsistent system.Side note: Any solution is of the form (x,y)
A particular plant root grows 1.5 inches per month. How many centimeters is the plant root growing per month? (1 inch = 2.54 centimeters). I WILL MARK BRAINLIEST~ PLEASE ITS THE LAST QUESTION!!
[tex]\huge\boxed{3.81\ \text{centimeters}}[/tex]
We simply need to convert 1.5 inches to centimeters.
Use multiplication:
[tex]1.5\cdot2.54=\boxed{3.81}[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Point A is at (0, 0). Using the transformation T: (x, y) (x + 2, y + 1), point A' = (2, 1). Hence:
[tex]AA'=\sqrt{(1-0)^2+(2 - 0)^2}=\sqrt{5}[/tex]
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
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After five science tests, Sonya's average score
is 89. If she gets a 95 on the sixth test, what is
her new average?
A. 89.50
B. 89.90
C. 90.00
D. 90.50
Answer:
C
Step-by-step explanation:
The sum of Sonya's 5 initial tests = 89*5 = 445.
445 + 95 = 540 (sum of the 6 tests)
Average = 540/6 = 90
Hence C
Answer:
C. 90.00
Step-by-step explanation:
We find average by adding up all values in a data set and dividing by the total number of values we have
We can say that Sonya got 89 for each test (it doesn't matter what each test score exactly was--you'll see why in a second)
So, we can add up 89 five times (5 tests have occured)
*I say add up, because that's what average is, but you can find this number by multiplying 89 · 5
89 · 5 = 445
(89 + 89 + 89 + 89 + 89 = 445)
Now, we need to add up our new value: 95
445 + 95 = 540
So, we can now divide 540 (sum of all values) by 6 (total number of values)
540 ÷ 6 = 90
So, C (90.00) is her new average
hope this helps! have a lovely day :)
Which composition of transformations maps figure EFGH to figure E"F"G"H"?
a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point G followed by a translation to the right
a translation to the right followed by a 180° rotation about point G
The composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
What is translation?A translation can be explained as the movement of a shape in a direction which could be up, down but the appearance of the figure remain unchanged in any other way.
And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.
Hence, composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
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Use the function below to find F(1)
Answer:
[tex]B: \frac{1}{2}[/tex]
Step-by-step explanation:
Plug 1 in as t
[tex]F(1) = 4 * \frac{1}{2^{3(1)}}[/tex]
Simplify the exponent 3*1
[tex]F(1) = 4 * \frac{1}{2^{3}}[/tex]
Cube the 2
[tex]F(1) = 4 * \frac{1}{8}[/tex]
Multiply:
[tex]F(1) = \frac{4}{8}[/tex]
Simplify:
[tex]F(1)=\frac{1}{2}[/tex]
Tony made 14 { L}14 L14, start text, space, L, end text of lemonade for a party. His guests drank 9,500 { mL}9,500 mL9, 500,m, L, end text of the lemonade.
How many milliliters of lemonade did Tony have left over?
Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,
Lemonade left = 14,000 - 9,500 = 4,500 ml
Hence, the lemonade left with Tony is 4500ml.
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Geometry
Find the area of the shaded region
Answer:
Area = 1125mi
Step-by-step explanation:
Area of sector = [tex]r^2 *\frac{\alpha }{2}[/tex]
[tex]r^{2} =5^{2} =25[/tex]
[tex]25*\frac{\alpha}{2}[/tex]
[tex]25*\frac{90}{2} =25*45=1125[/tex]
[tex]\alpha[/tex] = angle
[tex]r[/tex] = radius
radius is 5mi
in this case the angle is 90°
A = 1125mi
you can also solve by using circle area which is [tex]\pi r^{2}[/tex]
then divide by 4 because this is 1/4 of the circle.
Hope this helps
the mean value of land and buildings per acre from a sample of farms is $1400 with a standard deviation of $300 the data set has a bell shaped distribution assume the number of farms in the sample is 72 use empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1700
Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.
Hence, the number of farms out of 72 is:
0.68 x 72 = 49 farms.
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