The value of x which I suppose is the angle M is calculated to be 32°
Calculation of angles in a triangleIn a right-angled triangle KLM, it is a known fact that the sum of the three angles in any triangle is 180°.
Since angle L is a right angle and has a measure of 90°, we can find angle M by subtracting the sum of angles K and L from 180°.
Thus,
angle M = 180° - angle K - angle L
= 180° - 58° - 90°
= 32°
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If a solid has 6 faces and 12 edges, how many vertices does it have? A. 10 vertices B. 9 vertices C. 7 vertices D. 8 vertices
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
What is the equation of the line in slope-intercept form?
Answer:
The answer is the second choice.
Step-by-step explanation:
The slope is rise over run, which is 3/-1, which is -3, which goes before the x. The line hits the y axis at -1, so it is -3x–1
You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?
The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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100 POINTS!!! PLS ANSWER ASAP
The number of toys owned by eight classmates is shown below:
4, 3, 4, 5, 6, 6, 8, 4
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answer:
the answer for part A is. 5
the absolute deviation is. 1
Step-by-step explanation:
to find the answer for part A add all numbers and divide it by 8
4+3+4+5+6+6+8+5/840/85 is the answersFor part B
4-5= |-1|= 1
3-5= |-2|= 2
4-5= |-1| =1
5-5= |0| =0
6-5= |1 | =1
6-5= |1 | =1
8-5= |3| =3
5-5= |0| =0
Then add all the number and divided them by 8
1+2+1+0+1+1+3+0/89/89/8 is the answerMAY I GET BRAINLIEST
You invest $1500 in an account at interest rate r, compounded continuously.Find the time required for the amount to double and triple.(Round your answer to two decimal places). r=0.0355
The time required for the amount to double and triple are 19.53 and 30.95 respectively.
How to find the time required for the amount to double and triple?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]f(t) = P_{0}e^{rt}[/tex]
Where:
f(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;
[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]
Taking the natural log (ln) of both sides of the equation, we have:
0.0355t = ln(2)
Time, t = 19.53
Similarly, a function for the time required for the amount to triple is given by;
[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]
Time, t = 30.95
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20 pts
Need help asap!
The probability that the student is a sophomore, given that they are in work, is given as follows:
P(sophomore|work) = 30%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Total outcomes: 3 + 2 + 5 = 10 people at work.Desired outcomes: 3 sophomores at work.Hence the probability is obtained as follows:
P(sophomore|work) = 3/10 = 0.3 = 30%.
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Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+7cos(θ)−8=0
Select all that apply:
0.3
0.74
0.57
1.98
1.65
5.71
Answer:correct answer is 0.57
5.71
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 + 7u - 8 = 0
Now we can factor the quadratic:
(3u - 1)(u + 8) = 0
Therefore, either:
3cos(θ) - 1 = 0
cos(θ) = 1/3
or:
cos(θ) + 8 = 0
cos(θ) = -8 (not possible, since cos(θ) is between -1 and 1)
So, we have cos(θ) = 1/3. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:
θ = arccos(1/3)
Using a calculator, we find:
θ ≈ 1.2309 or θ ≈ 5.1102
Therefore, in radians, the solutions for θ are approximately:
1.2309 (which is less than 2π)
5.1102 (which is greater than 2π)
So the only answer that satisfies 0 ≤ θ < 2π is:
1.2309 (rounded to four decimal places)
Therefore, the answer is:
Question 1 (1 point)
Write an inequality for the sentence.
The stadium held less than 25,000.
B
O a
O b
9ba580e611107c96c9efb866417dc160.webm 64 KB
s> 25,000
$≤25,000
Oc $<25,000
The inequality that represents the sentence "The stadium held less than 25,000 people" is given as follows:
c < 25,000.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The amount is less than in this problem, hence the symbol is given as follows:
<.
As the amount is less than 25000, the inequality is given as follows:
c < 25,000.
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Carlos does 138 jumping jacks during gym class. John only does 89. How many more jumping jacks did Carlos do than John?
Answer:
Carlos did 49 more jumping jacks than John.
Step-by-step explanation:
Carlos = 138
John = 89
138 - 89 = 49
The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certain day, 269 people entered the park, and the admission fees collected totaled 1091 dollars. How many children and how many adults were admitted?
find the least common denominator
What is the solution to 3+x=x+3
Answer:
all real numbers
Step-by-step explanation:
if you subtract x from both sides, you get x=x. This is true for basically any number
Let A={a,b,k,s,u} and B={y,t,p,l,m,a}, find the least possible universal set for A and B
Answer:
The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.
The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.
Step-by-step explanation:
The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.
The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.
The graph of f(x) is shown below. - NW544 -3 (0.6) 2 1 -6-5-4-3-2-11 7 7 7 7 9 9 2 4 1 2 3 4 5 6 x If f(x) and its inverse function, f¹(x), are both plotted on the same coordinate plane, where is their point of intersection?
The point of intersection between a Inverse Functions and its inverse occurs at (2, 2).
The point of intersection between a function and its inverse occurs when the input and output values are the same for both functions.
To find the point of intersection, we need to find the value of x where f(x) = f-1(x).
In this particular case, we can see from the graph that the point of intersection occurs at (2, 2).
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I don't understand please help
The diameter of the circle is 396 units.
The length of the arc is 0.83π units.
How to find the diameter of the circle?The length of an arc of a circle is given by the formula:
L = θ/360 * πd
where θ is the measure of the angle and is the diameter of the circle
Given: θ = 80° and L = 88π
L = θ/360 * πd
88π = 80/360 * π * d
88 = 80/360 * d
80 * d = 88 * 360
80d = 31680
80d = 31680/80
d = 396 units
PART 2
If θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12
L = θ/360 * πd
L = 25/360 * π * 12
L = 0.83π units
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Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+3cos(θ)+7=0
Select all that apply:
1.77
0.48
1.4
3.77
2.99
2.51
Answer:3.77
2.51 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
-7u^2 + 3u + 7 = 0
Multiplying both sides by -1, we get:
7u^2 - 3u - 7 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 7, b = -3, and c = -7. Substituting these values, we get:
u = (3 ± sqrt(9 + 196)) / 14
u = (3 ± 5sqrt(5)) / 14
Therefore, either:
what is the volume of a hemisphere with a diameter of 8ft (rounded to the nearest tenth of a cubic foot)
well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}[/tex]
Simplify √ x + 3√ 3x − 5√ x.
Answer: -4rootx+3root3x
Step-by-step explanation:
think of the expression under the radicals as like terms, you can only add those that are the exact same 1-5=-4(rootx) can't do anything with the middle
Right triangle XYZ, has vertex angles at the coordinates, X(0, 0), Y(-3, 0) and Z(-3, 4). Its Image, triangle X'Y'Z' has ve
angles at the coordinates, X(3, -5), Y(0, -5), and Z'(0, -1). Describe the horizontal and vertical translations that map
triangle XYZ onto its image, triangle X'Y'Z'.
Oright 5; down 3
Oright 3; up 5
Oright 3; down 5
O left 5; up 3
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The horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z' include the following: C. right 3; down 5.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to map the two triangles, we would have to apply a vertical translation to f(x) by 5 units down and a horizontal translation by 3 units right.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The endpoints of WX are W(-5,-1) and X(2,6).
What is the length of WX?
A. 7
B. 14
C. 4√2
D. 7/2
Medication with strength 125 mg/5 mL has been ordered at 5 mg/kg. The patient weighs 134 lb. How much should be administered? (If less than 1, round to the nearest hundredth; otherwise, round to the nearest tenth.)
Rounding to the closest hundredth, the final result is 12.16 mL, which is the amount of the drug that should be administered.
The patient's weight must first be converted from pounds to kilograms.
1 lb = 0.453592 kg
Therefore, 134 lb = 60.78 kg
The dose must then be determined depending on the patient's weight:
60.78 kg times 5 mg/kg equals 303.9 mg.
Now that we know the medication's concentration, we need to determine how much to deliver.
25 mg/mL x 125 mg/5 mL
The dosage for 303.9 mg is as follows:
303.9 mg x 25 mg/mL = 12.16 mL
The final result, rounded to the closest hundredth, is 12.16 mL.
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Please help with my geometry.
Find the area of the shaded region.
Answer:
192pie
Step-by-step explanation:
To find the area of a circle, it is pie (3.14) times r². The radius is 24, so it is 24² times pie. The area is 576 pie. Now to find the area of the shaded, you would do 1/3 times the area. 1/3 of 576 is 192. The answer is 192pie
A circular table measures 2.5 feet across the diameter of its top. What is the approximate area of the table top. Use 3.14 for TT.
O 9.42 ft²
O 19.63 ft²
O 4.91 ft²
O 7.85 ft²
In △ABC, AB=6 cm, AC=15 cm, and m∠A=48°.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
The area of triangle ABC is : 33.44 cm²
What is the Area of a Triangle?The area of a triangle is the region enclosed within the sides of the triangle. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. The area of a triangle is expressed in square units, like, m2, cm2, in2, and so on.
We have the information from the question is:
In triangle ABC :
AB=6 cm,
AC=15 cm, and
m ∠A=48°.
We have to find the area of Triangle ABC
Area of triangle is : 1/2 × bc × (SinA)
Area of Triangle = 1/2 × 6 × 15 × (Sin 48° )
We know the value of Sin 48° is 0.7431
Area of Triangle = (1/2) × 66.88
Area of triangle = 33.44 cm²
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Need help now please!
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ at the given quadrant is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
The value of tan θ is calculated as follows;
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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The circle above has a radius of 3 cm. What is the area of the circle?
Answer:
Step-by-step explanation:
Answer:
28.27 CM ^2
Step-by-step explanation:
The formula for area of a circle is pi * r^2 where r = the radius.
Plugging the radius into the formula we get pi3^2, which equals 28.274 cm ^2 (and change)
How much will you have in our retirement account at the end of 2 years if you contribute $3,000 a year and have a 100% employer match? Assume a 9% annual return on your investments and end-of-year contributions.
0 $12,540.00
0 $6,000.00
Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)
Answer:
[tex]3 \frac{3}{4} \times 4 \frac{1}{2} \times 5 = \frac{15}{4} \times \frac{9}{2} \times 5 = \frac{675}{8} = 84\frac{3}{8} [/tex]
The volume is 84 3/8 cubic meters = 84.375 cubic meters.
What is the equation for the line of reflection?
On a coordinate plane, triangle A B C has points (6, 3.7), (5.4, 2), (1, 3). Triangle A prime B prime C prime has points (3.7, 6), (2, 5.4), (3, 1).
The equation of line of reflection of the coordinates is
y = x
What is line of reflection?Mathematics gives the concept of a line of reflection, otherwise known as a line of symmetry. This line acts as a mirror for any figure, where when shown through its reflection, the image becomes congruent to the initial shape.
In simpler words, the line of reflection is like an invisible partition that accurately segments a figure into two identical halves, each resembling the other in more ways than one.
The image is attached and upon investigation shows that the equation of y = x matches the equation of line of reflection
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What will be the answer?
A symbolic representation of the contrapositive is
letter D
Answer:
b
Step-by-step explanation:
