The Pythagorean inequality is given below.
Statement of Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
[tex]AC^{2}=AB^{2} +BC^{2}[/tex]
Let ABC be a triangle with the longest side opposite B
If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at BIf the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.If the square of the longest side is equal to the sum of the squares of the two shorter sides, then the triangle is right angled at B.We can also write as follows:
If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.
If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.
If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.
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What is the average rate of change? Problem in the picture
The average rate of change of the function f(x) over the interval (-1, 2) is; 3.
What is the difference quotient of the function over the given interval?As evident in the task content; the given function is as represented by the graph of f(x).
Hence, the average rate of change of the function over the given interval; (-1, 2) is;
= ( f (2) - f (-1) ) / (2 - (-1))
where; f (2) = 5 and f (-1) = -4.
Therefore, the average rate of change is;
= (5 - (-4)) / (2 - (-1))
= 9 / 3.
= 3.
Ultimately, the difference quotient of f (x) over the given interval is; 3.
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Given the following parallelogram, solve for x.
X =
(18x - 79) °
(7x + 9) °
can you please write out how you got the below answer?
Answer:
degree 2 and 10
Step-by-step explanation:
the degree of a polynomial is the value of the largest exponent of the variable.
r(x) = 10x² + 4x - 7
has largest exponent 2
this is a polynomial of degree 2
the leading coefficient is the coefficient of 10x²
that is leading coefficient is 10
A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.
The probability that at least 1 of the 4 cards drawn is a face card is 0.6.
How to find probability of 4 cards drawn?A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.
Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.
A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:
P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).
The likelihood that none of the four draws will produce a face card is:
P(no face cards are present) = (10/13)4 = 0.432
As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:
P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568
The chance, rounded to one decimal place, is roughly 0.6.
Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.
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Find the sum of the infinite geometric series, if possible. (Round your answer to three decimal places.)
∞
Σ
n = 0 6(0.75)n
STEP 1: Determine the first term of the infinite geometric series.
a1 =
24
STEP 2: Find the common ratio of the infinite geometric series.
r =
STEP 3: Based on your results from Step 1 and Step 2, the Sum of an Infinite Geometric Series Formula may be applied to this series. What guarantees the formula will work in this case?
The common ratio has an absolute value less than 1.
The first term of the series has an absolute value less than 1.
The common ratio has an absolute value less than the first term of the series.
The common ratio is less than the first term of the series.
The common ratio is less than one.
The first term of the series has an absolute value greater than the common ratio.
The first term of the series is positive.
STEP 4: Compute the sum of the series using the Sum of an Infinite Geometric Series Formula. Round your answer to three decimal places.
Sn =
STEP 1: a1 = 6.
STEP 2: r = 0.75
STEP 3: The common ratio is less than one.
STEP 4: The sum of the Sum of the Infinite Geometric series is Sn = 24
How to find the sum of the infinite geometric series?Since we have the expression for the sum of the infinite geometric series
[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]
STEP 1:
The first term of the infinite geometric series is 6. Thus, a1 = 6.
STEP 2:
The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75
STEP 3:
The common ratio is less than one.
Because Sn = a/(1 - r) is the formula we use when the common ratio is less than 1.
STEP 4:
Sn = a/(1 - r)
Sn = 6/(1 - 0.75) = 24
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For a certain year, the combined revenue of Nintendo and Sony was $44 billion. If that year the revenue for Sony was $12 billion more than the revenue for Nintendo, how much was the revenue for Nintendo?
Answer:
Nintendo's revenue was $21 billion
Step-by-step explanation:
A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score?
A. B in 3 three-credit classes
B. D in 1 three-credit class
C. in 1 four-credit class
D. C in 1 two-credit class
Weighed averages show that the student has a grade point average of 2.33.
How is the grade point determined?The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.
A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.
B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.
C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.
D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.
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Correct the one error. Just ten more day's and I'll be in London!
Just ten more days and I'll be in London!
Answer:
Just ten more days and I'll be in London!
the equation of a curve is given by
y=x^3/3+7x^2/2+10x+d, where d is a
constant. Find the possible values of d
when the x-axis is tangent to the curve
v=x^3/3+7x^2/2+10x+d.
Answer: A tangent to the x-axis means that the y-coordinate of the point of tangency is 0. So, we can find the possible values of d by setting y = 0 and solving for x:
0 = x^3/3 + 7x^2/2 + 10x + d
This is a cubic equation, so it can be solved using various methods such as factoring, completing the square, or using a numerical method such as the Newton-Raphson method. If the equation can be factored or the method used is numerical, there might be multiple possible values of d. If the method used is completing the square, there would be only one possible value of d.
However, without a specific method, it's not possible to find the exact value(s) of d. The possible values of d will depend on the specific solution method used to solve the equation.
Step-by-step explanation:
Please help me with this question please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.
In the given figure, there are two pairs of vertical angles~
That are :
[tex]\qquad \sf \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]
and
[tex]\qquad \sf \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]
Also, vertical opposite angles are equal in measure.
An angle measures 64.2° more than the measure of its complementary angle. What is the measure of each angle?
On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.
What are angles?An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.
An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.
x = first angle
Complementary angle is 14.2 degrees more than the cοmplementary angle.
First angle = x
Second angle = x + 14.2°
Complementary angle
x+x+14.2=90
2x+14.290
2x 90 14.2
2x = 75.8 x = 37.9
First angle is 37.9°.
Second angle will be:
x+14.2°
⇒37.9°+ 14.2°
⇒52.1°
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Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?
The numbers could be:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
Shawn rounded a number to the nearest tenth and got 6.5.
When he rounded it to the nearest whole number, he got 6.
Now,
The number = 6.45
Rounded to the nearest tenth = 6.5
Rounded to the nearest whole number = 6
The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
Thus,
The possible numbers are:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
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The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image
The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.
The new coordinates of B will be:
x-coordinate: 4 x (-2) = -8
y-coordinate: 4 x (-1) = -4
So the new vertex B' is (-8, -4).
The new coordinates of C will be:
x-coordinate: 4 x (2) = 8
y-coordinate: 4 x (-2) = -8
So the new vertex C' is (8, -8).
The new coordinates of D will be:
x-coordinate: 4(1) = 4
y-coordinate: 4(2) = 8
So the new vertex D' is (4, 8).
Therefore, the image of the resultant figure is given in the image below.
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someone pls help with this question
a² y² - 2aby + b²
Plot 1 1/2 and 2 2/5
The numbers on a number line is
|-------|-------|-------|-------|
0 1 2 3 4
* *
1 1/2 2 2/5
How to represent the numbers on a number lineFrom the question, we have the following parameters that can be used in our computation:
Plot 1 1/2 and 2 2/5
To plot 1 1/2 and 2 2/5 on a number line, we can follow these steps:
Find a suitable scale for the number line. Let's use the interval of 1 between each tick mark.Plot the first number, 1 1/2. 1 1/2 is halfway between 1 and 2Plot the second number, 2 2/5. This is between 3 and 3Read more about number line at
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For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets.
{10, 15, 14, 20, 11}
...
Step-by-step explanation:
A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.
To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.
To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.
Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.
Question 10 Part 1 of 3
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium
population continues to grow for a while, but then stops growing and begins to decline. The size of
the population at time t (hours) is b=8^6 +8^3t-8^2 t^2. Find the growth rates at t=0 hours,
t=4 hours, and t=8 hours.
The growth rate at t=0 hours is _____bacteria per hour
The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is 1,000,016.
How to calculate the number of bacteria over time?To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.
0 hours:
Population = 10^6 + (10^4)0 -(10^3)0^2
Population = 10^6 - 10^3
Population = 10^3 or 1,000
4 hours:
Population = 10^6 + (10^4)4 -(10^3)4^2
Population= 10^6 + 40,000 - 16,000
Population= 1,000,024
8 hours:
Population = 10^6 + (10^4)8 -(10^3)8^2
Population= 10^6 + 80,000 - 64,000
Population= 1,000,016
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how to solve this question
Rewrite the equation in Ax+By=C form
y-6=5(x+2)
Solve the following quadratic- like equation y 1/2-4y 1/4+3=0
The value of the quadratic like equation is given as y = 1 and y = 81.
What is substitution method?The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be favoured over the cross-multiplication method and the elimination method for straightforward equations without a lot of complicated calculations.
The equation is:
[tex]y^{\frac{1}{2} } - 4y^{\frac{1}{4} } + 3 = 0[/tex]
Using the exponent property we can write the equation as follows:
[tex](y^{\frac{1}{2} })^{\frac{4}{4} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{\frac{4}{2} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{2} - 4y^{\frac{1}{4} } + 3 = 0[/tex]
Now suppose the value of [tex]y^{\frac{1}{4} } = x[/tex].
x² - 4x + 3 = 0
x² - 3x - x + 3 = 0
x(x - 3) -1 (x - 3) = 0
(x - 1)(x - 3) = 0
x = 1
x = 3
Now, back substituting the value of [tex]y^{\frac{1}{4} } = x[/tex].
[tex]y^{\frac{1}{4} } = 1\\\\y^{\frac{1}{4} } = 3\\[/tex]
Raise to four on both sides of the equation we have:
y = 1
y = (3)⁴
y = 81
Hence, the value of the quadratic like equation is given as y = 1 and y = 81.
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four times the sum of the three consecutive even intergers is 240 more than six times the smallest integer.
Answer:
Step-by-step explanation:
Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".
Now we can set up the equation for the problem:
4 * (x + (x + 2) + (x + 4)) = 240 + 6x
Expanding the parentheses on the left side:
4 * (3x + 6) = 240 + 6x
Simplifying the left side:
12x + 24 = 240 + 6x
Subtracting 6x from both sides:
6x + 24 = 240
Subtracting 24 from both sides:
6x = 216
Dividing both sides by 6:
x = 36
So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.
8m
6m
10m
5m what is the area of this shape
Answer:
68 m²Step-by-step explanation:
we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.
6 * 8 + 4 * 5 = remember PEMDAS
48 + 20 =
68 m²
Simplify 8⁶÷8 Please im have trouble
Answer: 8^5
Step-by-step explanation: 8^6 is 8*8*8*8*8*8, so when you divide by 8 it cancels one of the 8s. Therefore you are left with 8*8*8*8*8 or 8^5.
[tex] {x}^{\frac{2}{3} }{ } = 64 [/tex]
Solve the following equation
The value of x in the given equation using laws of exponents is; x = 512
How to use Laws of Exponents?The different laws of exponents include;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
We have the equation as;
x^(2/3) = 64
We can write 64 as (∛512)²
This can be further expressed as;
512^(2/3)
Thus, we have;
x^(2/3) = 512^(2/3)
Thus, by identity rule;
x = 512
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Evaluate the expression:(2-1/2 • 7 1/3)^6
Write the answer in the most simplified form. Use fractions instead of decimal numbers.
The simplified form of the expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex] is [tex]6\frac{1}{8}[/tex].
What is the simplified form of the expression?Given the expression in the question:
[tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex]
To simplify the given expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex], first, rewrite the expression using the negative exponent rule:
[tex]( \frac{1}{2^{\frac{1}{2} }} * 7^{\frac{1}{3} )^6[/tex]
Next, combine the fractions:
[tex]( \frac{7^{\frac{1}{3} }}{2^{\frac{1}{2} }} )^6[/tex]
Simplify the numnerator:
[tex]\frac{49}{(2^{\frac{1}{2} })^6}[/tex]
Simplify the denpminator:
[tex]\frac{49}{8}\\ \\6\frac{1}{8}[/tex]
Therefore, the simplified form is [tex]6\frac{1}{8}[/tex]
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. For the first 40 hours Kayla works per week, she gets paid $12/hr. For each hour over 40
worked, she gets paid $18/hr. Write a piecewise function to represent her total pay with
respect to the number of hours worked. How much will she make for working 50 hours?
Answer:
$660
Step-by-step explanation:
If she gets $12/ an hour and works for 40 hours, 12*40=480. For every hour over 40, she gets $18/an hour, so if she works for 50 hours, you do 18*10 since she only worked 10 hours over 40. 18*10=180. To get the total amount, you do 480+180, which is 660.
Hope this helps! Please give brainliest!
Answer:
Therefore, Kayla will make $660 for working 50 hours.
Step-by-step explanation:
Let H be the number of hours worked in a week. The total pay can be represented as a piecewise function as follows:
f(H) =
12 * min(H, 40) +
18 * max(0, H - 40) if H >= 0
So, for H = 50 hours worked, we have:
f(50) = 12 * min(50, 40) + 18 * max(0, 50 - 40)
= 12 * 40 + 18 * (50 - 40)
= 480 + 180
= $660
Therefore, Kayla will make $660 for working 50 hours.
Which is true about the function y=−2x?
It is a nonlinear function because its graph passes through the origin.
It is a nonlinear function because its graph is a straight line.
It is a linear function because its graph passes through the origin.
It is a linear function because its graph is a straight line.
The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.
Which answer choice represents a true statement?It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?
On this note, since the graph of the equation is such that g
it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.
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A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of
100
100100 teachers from a statewide database containing every teacher, and they find
55
5555 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample
z
zz interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
The data is a random sample from the population of interest.
(Choice B)
B
n
p
^
≥
10
n
p
^
≥10n, p, with, hat, on top, is greater than or equal to, 10 and
n
(
1
−
p
^
)
≥
10
n(1−
p
^
)≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10
(Choice C)
C
Individual observations can be considered independent.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
What do you mean by SRS (Simple Random Sample)?Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.
To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
B) np^≥10n p^ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.
C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.
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1/4 (8x plus 2) = 20
Answer:
x = 9.75
Step-by-step explanation:
1 / 4 * ( 8x + 2) = 20
( 8x + 2) = 20 / (1/4)
8x + 2 = 20 * 4
8x + 2 = 80
8x = 78
x = 9.75
Answer:
x=39/4 (39 over 4 as a fraction)
Question 2
Answer: y =
<
-
Find the equation of the line with Slope = passing through the point (-35,10). Write your answer
in the form y = mz+ b.
I+
Submit Question
>
5
7
Write your answers as integers or as reduced fractions in the form A/B.
Question Help: Video Message instructor
An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 10 = -5/7(x - (-35))
y - 10 = -5/7(x + 35)
y - 10 = -5x/7 - 25
y = -5x/7 - 15
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