The measure of angle a is solved to be 22 degrees
How to find angle aWhen two secant lines intersect outside a circle the formula for the vertex angle at a is
To find the vertex angle at point A where two secant lines intersect outside a circle, you can use the following formula:
angle A = 1/2 * (measure of arc 1 - measure of arc 2)
let arc 1 = 140 degrees
arc 2 = 96 degrees
plugging in the values
angle A = 1/2 * (140 - 96)
angle A = 1/2 * 44
angle A = 22 degrees
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A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day. It is to be given in 3 doses each day. How much medication should they receive per dose? Remember, 2.2 pounds is equal to 1 kilogram. Round to the nearest whole number.
The amount of medication should they receive per dose is,
⇒ 363.6 mg
Given that;
A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.
And, It is to be given in 3 doses each day.
Hence, We get;
1 pounds = 1/2.2 kg
160 pounds = 160 x 1/2.2 kg
= 72.72 kg
Since, It is to be given in 3 doses each day.
Hence, The amount of medication should they receive per dose is,
⇒ 72.72 x 15 / 3
⇒ 363.6 mg
Thus, The amount of medication should they receive per dose is,
⇒ 363.6 mg
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which angles are corresponding angles?
angle1 and angle3
angle6 and angle8
angle5 and angle7
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:
−5,19,4,0,1
Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).
What is the statistics?Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.
To find the critical value for an 80% confidence interval, we need to determine the z-score corresponding to the level of confidence. We can use a standard normal distribution table or a calculator to find this value.
Using a standard normal distribution table, we can find the z-score that corresponds to an 80% confidence level by finding the area between the mean and the upper tail of 10%, which is (100% - 80%)/2 = 10%.
The area between the mean and 10% is 0.5 - 0.10 = 0.40. Using the standard normal distribution table, the z-score that corresponds to an area of 0.40 is approximately 1.28.
Hence, the critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).
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AM
CM
AM = CM
Which step is missing in the proof?
A. AMDA
B.
AMDA
OC. AMDA
D.
AMDA
CPCTC
definition of congruence
=
~
~
AMCB by ASA
AMBC by ASA
AMBC by SAS
ABMC by SAS
The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem
Given data ,
Let the two triangles be represented as ΔMDA and ΔMBC
Now , the measure of side MD ≅ MB ( given )
And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )
Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
So , ΔMDA ≅ ΔMBC by ASA theorem
Hence , the congruent triangles are solved
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Malachi asks students in his class, "How long does it take you to get to school?" The histogram
shows the data.
Which statement best describes the distribution?
Answer:
The distribution is symmetric
Step-by-step explanation:
Because in both sides it has the same structure, so that means that the value is the same in both sides
If a coin is flipped five times the probability of getting heads all five times is ______. Mark all that are true.
Answer: 1/2, the same as getting tails 5 times
Step-by-step explanation:
hope this helps
One factor of this polynomial is (x+8) x2+5x2-11x+104
The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13
What is a polynomial?A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.
The possible polynomial in the question is; x³ + 5·x² - 11·x + 104
The factor of the polynomial is; (x + 8)
The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.
The other steps of synthetic division can then be presented, summarily as follows;
Therefore;
-8 | 1[tex]{}[/tex] 5 -11 104
| [tex]{}[/tex] -8 24 104
1 -3 [tex]{}[/tex] 13 0
The factors of the polynomial
The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13
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A recipe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 1 gallon of milk?
Answer:
128 servings
Step-by-step explanation:
It takes 1 1/4 cups to make 10 servings
1 1/4 as a mixed fraction = 5/4
So 5/4 cups makes 10 servings
1 cup makes 10 ÷ 5/4
Use the fraction rule for division
a/b ÷ c/d = a/b x c/d
10 ÷ 5/4 = 10 x 4/5 = 8 servings from 1 cup
1 gallon = 16 cups
At 8 servings per cup, total number of servings for 16 cups
= 8 x 16 = 128 servings ANSWER
Of the 22 students in a classroom, 10 are transfer students, 7 are nursing students, 4 are AAS students and 1 student is undecided. If 5 students are chosen randomly, with replacement, find the probability that at least one student is a transfer student.
Solve for x. Round to the nearest tenth, if necessary.
8.69 is the length of the right angle.
Let's call the length you are trying to find x.
Using trigonometry, we know that:
cos(75) = x/9
Solving for x:
x = 9sin(75)
The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
Using a calculator to find the cosine of 75 degrees:
x ≈ 8.69
Therefore, the length you are trying to find is approximately 8.69.
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the visual fraction model shows the fractions of 1 cup of each kind of yogurt thats add to the blender
Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.
What is a fraction?Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.
Here,
A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.
For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.
You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.
You would have added
=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.
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i need help as soon as possible!
Answer:
2600This is a probability conversion problem.
WILL AWARD BRAINLIEST!!
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
Answer:
351 cm^3
Step-by-step explanation:
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
ChatGPT
Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:
AC = 2x * sin(35°)
Using the sine rule in triangle ABA, we have:
AB / sin(50°) = 18 / sin(80°)
Solving for AB, we get:
AB = 18 * sin(50°) / sin(80°)
The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:
V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)
Substituting the values we have calculated, we get:
V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)
V ≈ 351 cm^3
Therefore, the volume of the prism is approximately 351 cubic centimeters.
Pls help i rlly need help
Answer:
C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.
And for the second part,
1. No solution
5x+24=5x+25
24=25
It's false
2. One solution
12p-7=-3p+8
15p=15
P=1
3. One solution.
3x+20=5x
20 = 2x
X = 10
How do I find the parabola of the following. I tried to start. I do not know if I am on the right track, and if I am on the right track, what are the next steps to find and plot the parabola?
Thank you,
(x+4)(x+2)=0
((x+2)+4(x+2)
x^2 +2x+4x+8
X^2+6x+8
You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:
y = a(x - h)^2 + kwhere (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.
To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:
x^2 + 6x + 8 = 0x^2 + 6x = -8(x + 3)^2 - 9 = -8(x + 3)^2 = 1From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.
To find the value of a, you can compare the equation with the standard form of the quadratic equation:
y = a(x - h)^2 + kwhere h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:
-1 = a(-3 - (-3))^2 - 1-1 = a(0)^2 - 1a = 1So the equation of the parabola is:
y = (x + 3)^2 - 1To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.
two decimal places. A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr Mothapo. The actual amount of money that Mr Mothapo receives is R3 852,75. This is represented by the following timeline: R3 852,75 ? months 14% simple discount R4670,00 The amount of R4 670,00 is due to be paid back after
The value of amount of R4 670,00 is due to be paid back after 1.47 years.
We have to given that;
A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr. Mothapo.
And, The actual amount of money that Mr. Mothapo receives is R3 852,75.
Now, Let n be the loan period.
Hence, We get;
4670,00 = 385275 (1 + 0.14)ⁿ
1.212121 = (1.14)ⁿ
n log 1.14 = log 1.2121
n = 1.47
Thus, The value of amount of R4 670,00 is due to be paid back after 1.47 years.
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can someone help me do these qustions ( sorry if its hard to see) -(geometric sequence)
1. The geometric sequence is B. -1, 2, -4, 8.
2. The sixth term is 8192.
3. The next three terms are 1, 1/2 and 1/4.
4. The 10th term is 4374.
5. The eight term is 1/16.
6. The next three terms in the geometric sequence are -1/36 1/216, and - 1/1296
7. The 8th term or the sequence will be 4.
8. The 6th term of the geometric sequence is 2048.
How to calculate the valueThe 6th term of the sequence is:
a₆ = -2 * 4⁵ = -2 * 1024 = -2048
The common ratio of the sequence is:
r = 8/16 = 4/8 = 2/4 = 1/2
16 * (1/2) = 8
8 * (1/2) = 4
4 * (1/2) = 2
Therefore, the next three terms in the geometric sequence are 8, 4, and 2.
The common ratio of the sequence is:
r = 6/(-36) = -1/6
-1/6 * (1/6) = 1/36
1/36 * (1/6) = 1/216
-1/216 × 1/6 = -1 /1296
Therefore, the next three terms in the geometric sequence are -1/36, 1/216 and 1/1296.
The 8th term or the sequence will be:
= 512 × 0.5 × 0.5 × 0.5 × 0.5⁴
= 4
The 6th term of the geometric sequence is:
= 2 × 4 × 4 × 4 × 4 × 4
= 2048
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A sidewall of a building is shown below. Apply a formula to find the area of the wall.
Answer:1020 ft (squared)
Step-by-step explanation:
Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)
A vehicle purchased for $29800 depreciates at a constant rate of 7% per year. Determine the approximate
value of the vehicle 11 years after purchase.
Round to the nearest whole number.
The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413
Given data ,
Let the initial cost of the vehicle be = $ 29,800
Now , the rate of depreciation be r = 7 %
Let the number of years be n = 11 years
And , the exponential decay is given by the equation ,
x ( t ) = x₀ × ( 1 + r )ⁿ
On simplifying , we get
x ( 11 ) = 29800 ( 1 - 0.07 )¹¹
x ( 11 ) = 29800 ( 0.93 )¹¹
x ( 11 ) = 13,413.085
Hence , the cost of the vehicle after 11 years is A = $ 13,413
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HELP ASAP WILL GIVE BRAINLIEST
Use the graph to answer the question.
2
O
21/1/201
O
D'
IN
A
2
Determine the scale factor used to create the image.
C'
2.5
B'
D
A
11
C
2
В
B
Answer:
1/4
Step-by-step explanation:
The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.
Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
PLease help
what is the difference between an angle bisector and a segment bisector ?
The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.
What is an angle bisector?An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.
A segment bisector is defined as the line that divides a segment at the midpoint into two parts.
The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.
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A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took
13.5
m
2
13.5 m
2
13, point, 5, start text, space, m, end text, squared of material to build the cube.
What is the volume inside the giant sugar cube?
Give an exact answer (do not round).
The volume of the inside of the giant sugar cube would be = 3.375cm³
How to calculate the volume of a cube using the given surface area?To calculate the volume of a cube, the side length should first be determined from the surface area given.
But the formula for surface area of a cube = 6a²
That is;
surface area = 13.5cm²
a = ?
13.5 = 6(a)²
13.5/6 = a²
a = √13.5/6
= √2.25
= 1.5cm
Therefore the volume of the cube = a³
= 1.5³
= 3.375cm³
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Complete question:
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5m² of material to build the cube. What is the volume inside the giant sugar cube? Give an exact answer (do not round).
the perimeter of a triangle is 53 inches. the length of the one side is 15 inches the other two sides are congruent find the lengths
In the given Venn-diagram, if n(AUB) = 50, find n (A).
n°(A) = 2a
n°(B)=a
n(A[intersection]B)=20
Answer:
n(A U B) = n(A) + n(B) – n(A ∩ B)
putting values we get
50 = 2a + a - 20
solving eqn.
70 = 3a
a = 70 / 3
now n(a) = 2a
= 2 x 70/3
= 140/3
hence, n(a) = 140/3
A bank charges a monthly fee of 0.5% for a checking account. Lily’s account has $325 in it. Which function models the balance B of Lily’s account in dollars, as a function of time in months?
A. B(t) = 325(1 − 0.005)t
B. B(t) = 325(1 + 0.0005)t
C. B(t) = 0.05(1 − 3.25)t
D. B(t) = 325 + 12(1 + 0.0005)t
The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.
To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:
B(1) = 325 - 0.005(325)
Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:
B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))
We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:
B(2) = 325(1 - 0.005)²
Generalizing this pattern, we can see that after t months, the balance will be:
B(t) = 325(1 - 0.005)ᵗ
Therefore, option A is the correct function that models the balance of Lily’s account.
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For the following exercises,
(a) find the angle between 0 and 2π in radians that is coterminal with the given angle.
(b) find the reference angle of each one.
a)32π/13 b)-17π/6
The reference angle of given angles are -6π/13 and -5π / 6
To get coterminal angles, you simply have to add or subtract 2π.
a) 32π/13 =
= -32π/13 + 2π
= -32π + 26π / 13
= -6π/13
b) -17π/6 + 2π =
= -17π + 12π / 6
= -5π / 6
Hence the reference angle of given angles are -6π/13 and -5π / 6
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Evaluate the following 2x5➕24➗4-8
Answer: 8
Step-by-step explanation:
pemdas its not that deep
Find the perimeter of the triangle below.
31 cm
36.8 cm
9.73 cm
Answer:
77.53
Step-by-step explanation:
You just have to sum them up
Answer:
i think the answer is 77.53
Step-by-step explanation:
Can someone help me with this? I can't figure it out
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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