Answer:
Step-by-step explanation:
9. D
10.D
11.E
12.D
Answer:
9.
[tex]x^2-4\\(x-2)(x+2)[/tex]
10.
[tex]x^2-25\\(x-5)(x+5)[/tex]
11.
[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]
12.
[tex]x^2+100\\[/tex]
This polynomial cannot be factored by using the difference of squares method
question in pictures
The derivatives of the functions are listed below:
(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]
(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]
(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
How to find the first derivative of a group of functions
In this question we must obtain the first derivatives of each expression by applying differentiation rules:
(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]
[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex] Given[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}[/tex] Definition of power[tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex] Derivative of constant and power functions / Derivative of an addition of functions / Result(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]
[tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex] Given[tex]f(x) = (x + 3)^{\frac{1}{3} }\cdot (x + 5)^{\frac{1}{3} }[/tex] Definition of power[tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex] Derivative of a product of functions / Derivative of power function / Rule of chain / Result(c) f(x) = (sin x - cos x) / (x² - 1)
f(x) = (sin x - cos x) / (x² - 1) Givenf'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result(d) f(x) = 5ˣ · ㏒₅ x
f(x) = 5ˣ · ㏒₅ x Givenf'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result(e) f(x) = (x⁻⁵ + √3)⁻⁹
f(x) = (x⁻⁵ + √3)⁻⁹ Givenf'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant functionf'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]
[tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex] Given[tex]f'(x) = 7^{x\cdot\ln x} \cdot \ln 7 \cdot (\ln x + 1) + 7\cdot (x\cdot \ln x)^{6}\cdot (\ln x + 1)[/tex] Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex] Distributive property / Result(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]
[tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex] Given[tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex] Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result(h) f(x) = ㏑ (sin x) + sin (㏑ x)
f(x) = ㏑ (sin x) + sin (㏑ x) Givenf'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / ResultTo learn more on derivatives: https://brainly.com/question/23847661
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Evaluate 3x² - 4xy + 2y² - 1 for x = - 3 and y = 5
Answer:
[tex]3x^{2} - 4xy + 2y { }^{2} - 1 \\ 3 \times ( - 3) { }^{2} - 4 \times ( - 3) \times 5 + 2 \times 5 {}^{2} - 1 \\ (3 \times 9) - ( - 60) + 50 - 1 \\ 27 + 60 + 50 - 1 \\ 165 [/tex]
Answer: 136
Substitute -3 for x and 5 for y.
[tex]3x^2 - 4xy + 2y^2 - 1[/tex]
[tex]3(-3)^2-4(-3)(5)+2(5)^2-1[/tex]
[tex]3(9)-4(-15)+2(25)-1[/tex]
[tex]27+60+50-1[/tex]
[tex]87+50-1[/tex]
[tex]137-1[/tex]
[tex]136[/tex]
hope this helped!
Identify the vertex of the parabola ?
Step-by-step explanation:
second one
explanation: trust me bro
12. The base of a triangle with an area of 36 squared inches is 4.2 inches. What is the area of a similar
triangle whose base measures 5.6 inches?
The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches
Which method can be used to find the area of the similar triangle given the dimensions?Area of a triangle = (Base length × Height)/2
Area of the given triangle = 36 in.²
Base length of the given triangle = 4.2 inches
Base length of the similar triangle = 5.6 inches
Therefore;
Area of the given triangle = (Base length × Height)/2
Which gives;
36 = (4.2 × h)/2
Where;
h = Height of the given triangle
36 × 2 = 4.2 × h
[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]
Height of the given triangle, h = 17+ 1/7
The ratio of corresponding sides of similar triangles are the same, which gives;
[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]
Where;
h' = The height of the similar triangle
Which gives;
[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]
The area, A', of the similar triangle is therefore;
[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]
The area of the similar triangle A' = 64 in.²The area can also be obtained using the scale factor of area as follows;
(4.2/5.6)² = 36/A'Which gives;
A' = 64 square inchesLearn more about scale factors of calculations here:
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Which of the following represents
the graph of this equation?
y = 1/2|x|
The graph is shown in the attached image.
Solve the inequality
21≥t+10
The answer is t ≤ 11.
Subtract 10 from each side.21 - 10 ≥ t + 10 - 10t ≤ 11Question 3 of 10
If a circle has a diameter of 24 inches, which expression gives its area in
square inches?
OA. 12. T
OB. 242. T
O C. 122. T
OD. 24. T
SUBMIT
Answer:
OB:.242.T gives it's area in square inches
it took a 3D priner 10528 minutes to print 87 percent of a 3D print job. At this rate of speed how much time will take for the print to
reach 100 percent completion?
The time it would take for the print to reach 100 percent completion is 12,101 minutes 9 seconds.
What is time it would take to reach 100%?The mathematical operations that would be used to determine the required value are division and multiplication. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the process of determining the product of two or more numbers. The sign used to denote multiplication is ÷.
Other mathematical operations that are used to solve problems include addition and subtraction.
Time it would take to reach 100% completion = (minutes it takes to print 87% of the words x 100%) / 87%
Time it would take to reach 100% completion = (10,528 x 1) / 0.87 =
10.528 / 0.87
= 12,101. 15
= 12,101+ (0.15 x 60)
= 12,101 minutes 9 seconds
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Vanessa knows that about 20% of the students in her school are bilingual. She wants to estimate the probability that if 3 students were randomly selected, all 3 of them would be bilingual. To do so, she will use a spinner with 5 equally sized sections labeled as either "bilingual" or "monolingual". She will spin the spinner 3 times, record the results, and repeat the process 50 times.
How many of the 5 sections should she label "bilingual"?
How many of the 5 sections should she label "monolingual"?
Answer:
1 section should be labelled "bilingual".
4 sections should be labelled "monolingual".
Step-by-step explanation:
If 20% of students in the school are bilingual, then 80% of students in the school are monolingual, since 100% - 20% = 80%.
If the spinner is to be divided into 5 equally sized sections, with each section labeled as "bilingual" or "monolingual" to represent the corresponding proportion of students in the school, then:
Bilingual
20% of 5
= 20/100 × 5
= 100/100
= 1 section
Monolingual
80% of 5
= 80/100 × 5
= 400/100
= 4 sections
Therefore:
1 section should be labelled "bilingual".4 sections should be labelled "monolingual".Solve the following equation for W.
P=2L+2W
**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.
Answer: W = (P/2) - L
Step-by-step explanation:
Given equation
P = 2L + 2W
Factorize 2 out
P = 2 (L + W)
Divide 2 on both sides
P / 2 = 2 (L + W) / 2
P / 2 = L + W
Subtract L on both sides
(P / 2) - L = L + W - L
[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]
Step-by-step explanation:
To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):
[tex]\displaystyle{P = 2(L+W)}[/tex]
Next, we'll be dividing both sides by 2:
[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]
Then subtract both sides by L:
[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]
Therefore, we'll obtain W = P/2 - L.
Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.
So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.
Kieron is using a quadratic function to find the length and width of a rectangle. He solves his function and finds that
w = −15 and w = 20
Explain how he can interpret his answers in the context of the problem.
Answer:
Step-by-step explanation:
The correct value of w is 20 as the width of a rectangle must be positive. A quadratic function always has 2 zeroes and in a case like this the negative one is ignored.
A vector v has an initial (2,-3) point and terminal point (3,-4)
Write in component form.
The vector in component form is given by:
V = i - j.
How to find a vector?A vector is given by the terminal point subtracted by the initial point, hence:
(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)
How a vector is written in component form?A vector (a,b) in component form is:
V = a i + bj.
Hence, for vector (1,-1), we have that:
V = i - j.
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Write an absolute value equation to satisfy the given solution set shown on a number line
(infinity -1/2]u [-1/2 -1/2] u [1/2 infinity)
Find the area of figure below,
Answer: 57 cm²
Step-by-step explanation:
We can split this figure into two shapes: the rectangle on the left and the triangle on the right. We can find the area of each separately and add them to get the total area.
RectangleThe area of a rectangle is [tex]lw[/tex], where l is the length and w is the width. We can just multiply 8 and 6 to get the area of the rectangle.
[tex]A=8*6\\A=48[/tex]
TriangleThe area of the triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height. Here' the base would be 6 cm as opposite sides of a rectangle have the same measure, and the height is 3.
[tex]A=\frac{1}{2}(6*3)\\A=\frac{1}{2}(18)\\A=9[/tex]
TotalThe total area would just be the sum of the two separate areas.
[tex]48+9=57[/tex]
Hence, the area of the figure is 57 cm².
Answer: 57 cm^2
Step-by-step explanation:
To find the entire area of the figure, we have to find the area of the rectangle and the triangle and sum it up
The area of the rectangle is 6 * 8 = 48 cm^2
The area of the triangle is 1/2 * 3 * 6(Opposite sides of a rectangle have equal lengths) = 9 cm^2
So the area of the figure is 48 + 9 = 57 cm^2
he value of x?
ur answer in the box. need answer quickly! 35 points!
Answer:
x = 46 degrees
Step-by-step explanation:
180 - 134 = 46
Answer:
46°
Step-by-step explanation:
134 + x add to a straight line angle = 180
134+x = 180
x = 46
Miriam charges $5 per trip for deliveries plus $0.50 per mile, If x= the number of miles
Miriam drives for a trip and y = the total cost for a trip, which of these ordered pairs is a
solution to the equation that describes this situation? (1 Point)
(10, 10)
(2,7)
(12, 12)
(5, 6.5)
Answer:
(10,10)
Step-by-step explanation:
y = .5x + 5
If you put in 10 for x, we get 10 for y.
y = .5(10) + 5
y =5 + 5
y = 10
When x is 10, y is 10 (10,10)
Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)
16
0
sin
x
dx, n = 4
Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],
[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]
with midpoints 2, 6, 10, and 14, respectively.
Then with the midpoint rule, we approximate the integral to be about
[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]
Solve for y.......
[tex]6 = 2(y + 2)[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
y = 1[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \:6 = 2(y + 2)[/tex]
[tex] \qquad❖ \: \sf \:(y + 2) = \cfrac{6}{2} [/tex]
[tex] \qquad❖ \: \sf \:y + 2 = 3[/tex]
[tex] \qquad❖ \: \sf \:y = 3 - 2[/tex]
[tex] \qquad❖ \: \sf \:y = 1[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Value of y = 1Perform the operation and
simplify.
3
x - 3
5
x + 2
-2x + 21
x² + [ ? ]x + [
Answer: -1
Step-by-step explanation:
Here, we are subtracting two fractions; therefore, we must make the denominators the same by finding the least common multiple. Since we have x - 3 for one denominator and x + 2 for the other, we don't have any common factors. Hence, the least common multiple would be their product.
[tex](x-3)(x+2)\\x(x-3)+2(x-3)\\x^2-3x+2x-6\\x^2-x-6[/tex]
The question is looking for the coefficient of the second term. Since there is just a negative sign in front of the x, the "?" can be filled with either a negative sign or a -1.
HELPPPP PLSSSSSss!!!!!!!
Answer:(5-1)(7-1)
Step-by-step explanation:
We have give 4 numbers that are 1,1,5,7. we have to apply operations on it to make it 24.
Solution :» ( 7 - 1) × (5 - 1)
» (6) × (4)
» 24
Here's our answer..!!
4x-12y=-20 substitution method
If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Given two equations x-2y=5 and 4x+12y=-20.
We are required to find the value of x and y through substitution method.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.
They can be solved as under:
x-2y=5---------------1
4x+12y=-20--------2
Finding value of variable x from equation 1.
x=5+2y--------------3
Use the value of variable x in equation 2.
4x+12y=-20
4(5+2y)+12y=-20
20+8y+12y=-20
20y=-20-20
20y=-40
y=-40/20
y=-2
Use the value of variable y in equation 3.
x=5+2y
x=5+2*(-2)
x=5-4
x=1
Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Question is incomplete as it should include one more equation x-2y=5.
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The formula for the perimeter of a rectangle is 2L + 2W = P (L = length, W = Width and P = Perimeter.) The perimeter of a rectangular garden is 400 feet. If the length of one side of the garden is 120 feet, what is the width of one side of the garden?
We conclude that the width of the rectangular garden is 80 feet.
How to get the dimensions of the garden?Let's define the variables:
L = length of the garden.W = width of the garden.The perimeter of a rectangle of length L and width W is given by the simple formula:
P = 2*(L + W)
The perimeter is equal to 400ft, then:
400ft = 2*(L + W)
And we know that the length is 120ft, then:
L = 120ft.
Replacing the length in the perimeter equation we get:
400ft = 2*(120ft + W)
Now we can solve this linear equation for W.
400ft/2 = 120ft + W
200ft = 120ft + W
200ft - 120ft = W
80ft = W
We conclude that the width of the rectangular garden is 80 feet.
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Relate ratios in right triangles
Consider right triangle ADEF below. Which Expressions are equivalent to cos(E)?
Answer:
B
Step-by-step explanation:
Cos is the adjacent side over the hypotenuse. The adjacent side to <E is side ED. The hypotenuse is side EF. ED/EF. They do not go right out and give you this choice, but you see that B says the same thing.
If Emery has $1,400 to invest at 5% per year compounded monthly, how long will it be before he has $2,400? If the compounding is
continuous, how long will it be? (Round your answers to three decimal places.)
Answer:
Step-by-step explanation:
(1400x14.5x5%) + 1400 =2415
Answer: 14.5 months
Hello please help asap!! i will mark brainliest and this is worth 20 points!!!!! tysm
The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.
What is the least number of colors?From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.
After all, it notes no two touching sections, not adjacent sections.
There is no equation to calculate this requirement with respect to the total number of sections.
Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.
If a square were to be this starting shape that have same color as that color of the square.
Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.
Like that the remaining figures are given colors.
Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.
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If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
a
f(x) dx ≤ M(b − a).
Use this property to estimate the value of the integral.
⁄12 7 tan(4x) dx
It's easy to show that [tex]7\tan(4x)[/tex] is strictly increasing on [tex]x\in\left[0,\frac\pi8\right][/tex]. This means
[tex]M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3[/tex]
and
[tex]m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7[/tex]
Then the integral is bounded by
[tex]\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)[/tex]
[tex]\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}[/tex]
Given that a function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6, select the statement that could be true for g.
The given statement that's true about the function is g(-13) = 20 is true for g.
How to illustrate the function?From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.
Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.
g(-13) = 29
x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.
g(0) = 2.
This isn't true because it is given that g(0) = 2
In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.
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9) If m/1 = 45° and 21 and 22 are complementary angles. Find m22.
❄ Hi there,
keeping in mind that the sum of complementary angles is 90°,
set up an equation, letting [tex]\angle2[/tex] be x –
[tex]\triangleright \ \sf{\angle1+x=90}[/tex] {and we know that [tex]\boxed{\angle1=45}[/tex]}
[tex]\triangleright \ \sf{45+x=90}[/tex]
[tex]\triangleright \ \sf{x=90-45}[/tex]
[tex]\triangleright \ \sf{x=45}[/tex]
[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]
__________
Keeping in mind that a right angle is 90°,
set up an equation, letting [tex]\angle1[/tex] be x:
[tex]\triangleright \ \sf{x+\angle2=90}[/tex] {and we know that [tex]\boxed{\angle2=63}[/tex]}
[tex]\triangleright \ \sf{x+63=90}[/tex]
[tex]\triangleright \ \sf{x=27}[/tex]
[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]
❄
For a standard normal distribution, find:
P(-1.64 < z < 0.2)
For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876
How to find the p-value from 2 z-scores?
We want to find the p-value between 2 z-scores expressed as;
P(-1.64 < z < 0.2)
To solve this, we will solve it as;
P(-1.64 < z < 0.2) = 1 - [P(z < -1.64) + P(z > 0.2)]
From normal distribution table, we have that;
P(x < -1.64) = 0.050503
P(x > 0.2) = 0.42074
Thus;
P(-1.64 < z < 0.2) = 1 - (0.050503 + 0.42074)
P(-1.64 < z < 0.2) = 0.52876
Thus, For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876
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121 slabs . How many slabs will she need to lay in each row to make a square
She needs to lay 11 slabs on each row to make a square
How to determine the number of slabs in each row?The total number of slabs is given as:
Total = 121 slabs
Let this represent the area of the slab.
The area of a square is calculated as:
Area = Length^2
Substitute the known values in the above equation
Length^2 = 121
Take the square root of both sides
Length = 11
Hence, she needs to lay 11 slabs on each row to make a square
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