The value of a is 20.
What are Angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Given that,
HL is perpendicular to HJ
m ∠2 = (a + 15)°
and
m ∠3 = (a + 35)°
If HL and HJ are perpendicular,
Then,
m ∠2 + m ∠3 = 90°
(a + 15)° + (a + 35)° = 90°
Now, solve for a
(a + 15)° + (a + 35)° = 90°
a + 15 + a + 35 = 90
a + a = 90 - 15 - 35
2a = 40
a = [tex]\frac{40}{2}[/tex]
a = 20.
Hence, the value of a is 20
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Find the range of the following
function given that
ƒ(x) = x² − 1
Domain: -2
Answer:
Hope the picture will help you
How many 135-inch-thick books can fit on a 1412-inch-long bookshelf?
You can fit ? books on the bookshelf.
What are the perimeters of this
perimeter of triangle is = 3 + 5 + 4 = 12 cm
perimeter of rectangle is = 2( 3 + 6 ) = 18 cm
perimeter of parallelogram is = 2 (5+7) = 24 cm
What is perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is referred to as its perimeter. Perimeter calculations have many practical applications.
Calculationperimeter of triangle is = 3 + 5 + 4 = 12 cm
perimeter of rectangle is = 2( 3 + 6 ) = 18 cm
perimeter of parallelogram is = 2 (5+7) = 24 cm
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use the range rule of thumb to find the minimum usual value μ–2σ and the maximum usual value μ 2σ. enter answer as an interval using square-brackets only with whole numbers.
The range thumb rule The minimum and maximum values for the usual value, which is two, are 812.14 and 885.85, respectively.
Range thumb rule: what is it?An efficient way to calculate the range from the standard deviation is to use the range rule of thumb. The range is normally around four times the standard deviation, according to this information. Inferring that your range is around eight if your standard deviation is 2, for example.
As an illustration of a binomial distribution, we'll utilize seeds.
According to given data;
Let "X" represent the number of tomato seeds that actually germinate based on the data provided.
With the knowledge provided above, we can now determine the:
The median number of seeds that we may anticipate to germinate
standard deviation (σ): sqrt of n*p*(1-p)
Once you calculate the mean and standard deviation, you can calculate the minimum usual value and the max usual value.
Now, in your problem:
n = 1415
p = 3/5
so,
the mean would be: (1415)(3/5) = 849
the standard deviation would be: sqrt (mean)(1-3/5) = 18.4282
Next, we find the minimum and maximum usual values according to the equations you gave:
minimum: mean - 2(standard deviation)
= 849 - 2(18.4282)
= 812.1436
maximum: mean + 2(standard deviation)
= 849 + 2(18.4282)
= 885.8564
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PLEASE HELP ASAP!!!!!
The definition for the function is y = {-2x +1 x < 1 ; -x + 2 x ≥ 1. The correct option is b.
Equation of a functionFrom the question, we are to determine the equation for the function
First, we will determine the equation for when x < 1
Picking the points (-1, 3) and (0, 1)
Using the formula,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
(y - 3) / (x - -1) = (1 - 3) / (0 - -1)
(y - 3) / (x + 1) = -2 / (0 + 1)
(y - 3) / (x + 1) = -2 / 1
(y - 3) / (x + 1) = -2
y - 3 = -2(x + 1)
y - 3 = -2x - 2
y = -2x - 2 + 3
y = -2x + 1
Thus,
When x < 1, the function is y = -2x + 1
Now, determine the equation for when x ≥ 1
Picking the points (1, 1) and (2, 0)
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
(y - 1) / (x - 1) = (0 - 1) / (2 - 1)
(y - 1) / (x - 1) = -1 / 1
(y - 1) / (x - 1) = -1
y - 1 = -1(x - 1)
y - 1 = -x + 1
y = -x + 1 + 1
y = -x + 2
Thus,
When x ≥ 1, the function is y = -x + 2
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point F is on line segment EG. given FG = 8, EF = 2x + 4, and EG = 4x - 10, determine the numerical length of EF
Step-by-step explanation:
equate the two small distances to the total distance and solve for x
Which of the following statements best describes the value of the expression 2x – 7, when x = 5?
A. The result is not a whole number.
B. The result is a prime number.
C. The result is a composite number.
D. The result is a whole number that is neither prime nor composite.
7TH grade math
The best description of the value of the expression 2x - 7, when x = 5 is B. The result is a prime number.
What is a prime number?A prime number cannot be divided by another number except by itself or 1.
Common prime numbers include 2, 3, 5, 7, 11, 13, 17, and 19.
The value of 2x – 7, when x = 5 is 3.
3 is a prime number as well as a whole number, but it is not a composite number.
Thus, we can conclude that the result of solving the expression is the prime number 3.
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804
X 79
Explain step by step
The correct answer to task 804 × 79 is 63,516.
Understanding the multiplication of numbersWhen we multiply a number and another together, or a number and a variable, or even a variable with another variable, we mean the product of the two factors. The multiplication sign is " × " .
The step by step explanation of the task above is given below:
804 × 79 = 63,516.
Another example of Multiplication is
40 × 2 = 80.
The product of a and b also means Multiplication.
a and b means a × b = ab.
The product or the multiplication of g and 5 means g × 5 = 5g.
In conclusion, from the detailed information and explanation given above, the product of 804 × 79 is 63,516.
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Need help with this question!!!!
Using the exterior angle of a polygon theorem, the value of the missing angle is 58°
Calculating the value of a missing angleFrom the question, we are to calculate the value of the missing angle.
From the given information, the missing angle is (3x -2)°.
To calculate the value of the missing angle,
First, we will determine the value of x
From the Exterior angle of a polygon theorem, we can write that
90° + (3x + 12)° + (4x - 10)° + (3x - 2)° + 70° = 360°
(3x + 12)° + (4x - 10)° + (3x - 2)° = 360° - 70° - 90°
3x° + 12° + 4x° - 10° + 3x° - 2° = 200°
10x° = 200° + 2° + 10° - 12°
10x° = 200°
x = 200/10
x = 20
The missing angle is (3x -2)°
Substitute the value of x
(3(20) -2)°
= (60 -2)°
= 58°
Thus,
The missing angle measure is 58°
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Fully simplify 5√/20 - 4√5
[tex]5\sqrt{20} = 5\sqrt{4.5} = 5.2\sqrt{5} = 10\sqrt{5}[/tex]
[tex]10\sqrt{5} - 4\sqrt{5} = 6\sqrt{5}[/tex]
Name the property shown and explain
in a complete sentence supporting
your answer choice.
a (b + c) = ab+ac
what is x and what is the am of the segment
Answer:
-0.5 or -1/2
Step-by-step explanation:
(5x) + (3x+4) = 8x+4
8x+4 = 0
8x = -4
x = -0.5
Hope that helps
question is in the photo
The values for the parabola are found as-
Focus, a = 4x axis vertex; h = 5y-axis vertex; k = 8What is meant by the parabola?A parabola is a curve equation in which a point on a curve is equidistant out of a fixed point and a fixed line. The fixed point is known as the parabola's focus, and also the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie just on fixed line.The focus of the parabola is the point (a, 0).The parabola's directrix is the line sketched parallel to a y-axis and passing through point (-a, 0). The directrix is perpendicular to a parabola's axis.For the given question.
The total horizontal distance covered by water is 10 feet.
The maximum height attained by nozzle of water is 8 feet.
Thus, the vertex of parabola (h, k) = (5, 8)
The nozzle was 4 foot above the ground, a = 4.
The equation of parabola becomes;
y = a(x - h)² + k
y = 4(x - 5)² + 8
Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.
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Choose the multiplication problem that matches this model: I Dan studied for of an hour for 4 days in a row. How many hours did he study? Dan studied for 2 hours for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study?
The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.
What is multiplication?The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.
If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.
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3 of your 5 teachers are females what percent of your teachers are females
Answer: 60% of your teachers are female
Step-by-step explanation: 3 out of 5 is 60%
Consider the equation shown.
24
2"
What is the value of n?
Applying the rules of exponents, the value of n in the equation given is calculated as: n = 8.
How to Apply the Rules of Exponents?The product rule of exponents says that when the base are the same, add their exponents together.
For example, m × m² = m^(1 + 2) = m³.
The exponents are 1 and 2. The expression has similar base of m. Therefore, to multiply m and m² together, we would simply add their exponents together while the final result will be the same base.
Also, the negative rule of exponents states that we subtract their exponents if they have he same base.
For example:
m³/m² = m³ ÷ m² = m^(3 - 2) = m.
Given the equation:
[tex]\frac{4^3 \times 8^2}{2^n} = 2^4[/tex]
Simplify the bases to make all equal
= [tex]\frac{2^{(2)(3)} \times 2^{(3)(2)}}{2^n} = 2^4[/tex]
= [tex]\frac{2^{6} \times 2^{6}}{2^n} = 2^4[/tex]
Apply the product rule and the negative rule of exponents to find the value of n in tye equation:
[tex]2^{(6 + 6 - n)} = 2^4\\\\2^{(12 - n)} = 2^4\\\\[/tex]
The bases will cancel each other:
12 - n = 4
Subtract 12 from both sides
12 - n - 12 = 4 - 12
-n = -8
Divide both sides by -1
n = 8
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jaylin has a wooden cube which is painted blue on the outside. she cuts the cube into $1000$ identical cubes, some of which have some sides painted blue, then rolls the resulting cubes like dice. the probability that no blue faces land up after jaylin rolls the $1000$ cubes can be expressed as $2^a \times 3^b \times 5^c$ where $a$, $b$ and $c$ are integers. what is the value of $a b c$?
The probability is a + b + c = -382
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Every cube's side is [tex]\sqrt[3]{1000}[/tex] = 10
Since there are 512 unpainted cubes within, the likelihood is 1⁵¹² = 1
There are 8 corners, and each one has a chance of 3 / 6 = 1 / 2 = 2⁻¹ so the probability is 1⁸ / 2 = 1 / 2⁸
There are 8 * 12 = 96 edge pieces (12 edges total, with 8 on each edge; each cube has a probability of 4 / 6 = 2 / 3, so the probability is 2⁹⁶ / 3 = 2⁹⁶ / 3⁹⁶
There are 8 * 8 * 6 = 384 center cubes, each having a chance of 5 / 6, so the probability is 5³⁸⁴ / 6 = 5³⁸⁴ / 6³⁸⁴ = 5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)
So, the probability is:
(1 / 2⁸) * (2⁹⁶ / 3⁹⁶) * [5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)]
= (5³⁸⁴ * 2⁹⁶) / (2³⁹² * 3⁴⁷⁰)
= 5³⁹⁴ * 2⁹⁶ * 2⁻³⁹² * 3⁻⁴⁷⁰
= 5³⁸⁴ * 2⁻²⁹⁶ * 3⁻⁴⁷⁰
Thus, a + b + c = -382
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If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called what?.
Answer: The correct answer is the Law of Large Numbers
Step-by-step explanation:
Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.
However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.
The more trials you do, the more likely you will get close to the theoretical value.
marlena surveyed classmates and found that the ratio of the numbers of text messages sent by girls varies directly with the number of texts sent to boys. The girls sent 27 texts for 9 texts sent by the boys.How Many texts did the girls send if the boys sent 7 texts
Choose a rational number expressed as an infinite periodic decimal greater than 0.6(3) and less than 0.64.
Answer:
0.635
Step-by-step explanation:
This is half way between 0.63 and 0.64.
Hope this helps!
a scale drawing of a rectangular building is 4 inches wide and 5 inches long. the actual building is 240 yards wide. what is the area of the actual building in yards
Answer:
72,000 yards
Step-by-step explanation:
The scale factor can be found by doing:
[tex]240 \div 4 = 60[/tex]
This means that 60 is the scale factor. You can apply the scale factor to the length of the rectangular building, meaning that the length of the actual building is:
[tex]5 \cdot 60 = 300[/tex] yards
So, if the building is 240 yards wide, and 300 yards long. You can find the area of the actual building just like any other rectangle using:
[tex]A = l \cdot w[/tex]
(Area = length * width)
So, the final answer is:
[tex]A = 300 \cdot 240\\ A= 72,000[/tex]
This means that the area of the actual building is 72,000 yards.
Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to 1.
The quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is:
x² + (2/3)x - 1/9 = 0
We have been given the roots of quadratic equation.
(-1 - √2)/3 and (-1 + √2)/3
We need to find the quadratic equation.
Since (-1 - √2)/3 and (-1 + √2)/3 are roots, (x - (-1 - √2)/3) and (x - (-1 + √2)/3) must be the factors of the quadratic equation.
So, the required quadratic equation would be,
(x - (-1 - √2)/3) * (x - (-1 + √2)/3) = 0
x[x - (-1 + √2)/3) ] - ( (-1 - √2)/3) [x - (-1 + √2)/3] = 0
x² - x(-1 + √2)/3 - x(-1 - √2)/3 + [(-1 - √2)(-1 + √2)]/9 = 0
x² - x(-2/3) + (1 - 2)/9 = 0
x² + (2/3)x - 1/9 = 0
Therefore, the quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is: x² + (2/3)x - 1/9 = 0
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Whats the answer for the math problem
Answer:
the answer is -60........
Answer:
-60! 1560 divided by 26 is 60, but any negative divided by a positive is a negative, so the product will be negative as well.
Step-by-step explanation:
Hope it helps! =D
What is the solution to the given equation 2(y-5)=14
Answer: y=12
Step-by-step explanation:
Distribute
Add 10 to both sides
Simplify.
Answer: y = 12
Step-by-step explanation:
2 ( [tex]y\\[/tex] - 5 ) = 14
2[tex]y\\[/tex] - 2 · 5 = 14
2[tex]y\\[/tex] - 10 = 14
(2[tex]y\\[/tex] - 10) + 10 = 14 + 10
2[tex]y\\[/tex] = 24
[tex]\frac{2y}{2} = \frac{24}{2}[/tex]
The range of a set of numbers is 19.
The minimum value is 9.
What is the maximum value?
If the range of the data set is 19. Then the maximum value of the set will be 28.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
The range of the data is the difference between the maximum number to the minimum number. Then the formula is written as,
Range = Maximum value - Minimum value
The range of a set of numbers is 19. And the minimum value is 9.
Then the maximum value of the set is calculated as,
Range = Maximum value - Minimum value
19 = Maximum value - 9
Maximum value = 19 + 9
Maximum value 28
If the range of the data set is 19. Then the maximum value of the set will be 28.
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katrina can arrange the chairs in the classroom in 5 minutes. one day peter helped her and took both of them 2 minutes to arrange the chairs. how long will it take peter to arrange the chairs all by himself?
The time taken by Peter to arrange the chairs all by himself is 10/3 minutes.
Given that :-
Katrina can arrange the chairs in the classroom in 5 minutes.
One day peter helped her and took both of them 2 minutes to arrange the chairs.
We have to find the time taken by Peter to arrange the chairs all by himself.
LCM (5,2) = 10
Let the total work of arranging the chairs is of 10 units.
We know that,
Efficiency of a person = Total Work/Time taken by person
Hence,
Efficiency of Katrina = 10/5 = 2 units
Efficiency of Katrina + Efficiency of Peter = 10/2 = 5 units
Hence,
Efficiency of Peter = 5 - 2 = 3 units
Hence, time taken by Peter to arrange the chairs all by himself = 10/3 minutes.
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What is the surface area of a cylinder that has a radius of 5 m and a height of 13 m?
Surface area of a cylinder= 2πr(h+r)
=2×22/7×5×(13+5)
=31.43×(18)
=565.74meter squared
what is the SURFACE AREA
Answer:
164 cm
Step-by-step explanation:
(4x6) / 2= 12
12x2=24 because there are 2 triangles
10x6=60 for the rectangle
(4x10) x 2=80 for the sides
80+60=140
140+24=164
A zoo has an agreement with the local farmers. They sell the daily waste from the elephants to the farmers for $5.00 per pound. If the amount of waste produced by the elephant on a given day is at the 10th percentile of the distribution of waste, how much money would the zoo make selling the waste that day?
The amount of money would be $1115.45 the zoo makes selling the waste that day.
What is Z - score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.
To determine the amount of money would the zoo make selling the waste that day.
P(z ≤ z₀) = 0.1
z₀ = -1.28
⇒z₀ =(x₀ -μ ) / σ
Substitute the values and solve for x₀,
⇒ -1.28 =(x₀ -250 ) / 21
⇒x₀ = (-1.28)×21 - 250
⇒x₀ = 223.09
So the amount of money would be as :
⇒ 223.09 × 5
⇒ 1115.45
Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.
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If you double a number and then add 28 , you get
{4}{9} of the original number. what is the original number?
In this mathematical expression, the original number is 4.
How is the original number determined?We can use a mathematical equation to work out the original number.
A mathematical equation uses variables, numbers, and constants to show that two values are equal.
Mathematical equations connect two mathematical expressions using the equal sign (=).
Let the original number = x
According to the statement:
2x + 28 = {4}{9}
This implies that:
2x + 28 = 36
Subtracting 28 from both sides gives:
2x = 8
x = 4
Thus, the original number is 4.
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