Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].
How to estimate the sum of 9/16 and 5/4?Find the least common denominator or LCM of the two denominators:
LCM of 4 and 16 exist 16.
Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.
For the 1st fraction, since 16 × 1 = 16,
9/16 = (9 × 1) / (16 × 1) = 9/16
For the 2nd fraction, since 4 × 4 = 16,
5/4 = (5 × 4) / (4 × 4) = 20/16
Add the two like fractions, then we get
(20/16) + (9/16) = (20 + 9)/16 = 29/16
So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]
In mixed form: [tex]$1 \frac{13}{16}[/tex].
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There are 1000 students at a college. In January, æ of these students had passed
their driving test.
Between January and April, the number of students who had passed their driving
test increased by 20%, and the number of students who had not passed
decreased by 5%. No one left or joined the college during this time.
a) Explain why the number of students who had not passed their driving test yet
was 0.95(1000 - x) in April.
b) Hence explain why 1.2x +0.95(1000-x) = 1000.
c) How many students had passed their driving test in January?
a) In April, the number of students who had not passed their driving test decreased by 5%.
b) The equation is 1.2x + 0.95(1000 - x) = 1000.
c) 200 students passed their driving test in January.
a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).
In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
b)
The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).
The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.
c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.
Expanding the equation, we get:
1.2x + 950 - 0.95x = 1000
0.25x = 50
x = 200
Therefore, 200 students passed their driving test in January.
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If the equation is an identity
The equation is an identity is discussed below.
An identity is a mathematical equation that holds true for all values of the variables involved.
In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.
For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.
When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.
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If you flip two coins 68 times, what is the best prediction possible for the number of times both coins will land on heads?the number of times it will land on tails?
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.
If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.
What is the probability of getting two heads?The possible outcomes when two coins are flipped are;
head - head = HH
tail - tail = TT
Head and tail = HT
Tail and head = TH
The probability of getting two heads = 1/4
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;
Expected value = (68 flips) x (1/4 probability of getting HH) = 17
The probability of getting two tails = 1/4
Expected value = 68 x 1/4 = 17
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The figure below shows a triangle with vertices, a and B on a circle and vertex c outside it. Side ac is tangent to the circle. Side bc is a secant intersecting the circle at point x. What is the measure of angle acb?
1.32
2.60
3.28
4.16
The measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
The measure of angle ACB can be determined using the properties of tangents and secants intersecting a circle.
Since side AC is tangent to the circle, angle BAC is a right angle (90 degrees).
According to the tangent-secant theorem, the measure of angle ACB is equal to half the difference between the intercepted arcs AB and AX.
Since angle BAC is a right angle, the intercepted arc AX is a semicircle, which means its measure is 180 degrees. The intercepted arc AB is an arc of the circle and is less than 180 degrees since it is not a full circle.
Therefore, the measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
To find the exact measure, more information is needed about the length of arc AB or the relationship between the lengths of the sides of the triangle. Without this additional information, we cannot determine the precise measure of angle ACB.
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PLEASE I NEED HELP !!!!!
The weight of a pitaya seed in standard form is [tex]1 \times 10^-^6[/tex]ounce.
In standard form, the weight of a pitaya seed is expressed in scientific notation, where the number is a decimal between 1 and 10, and the exponent is a power of 10. The weight of a pitaya seed is given as [tex]1 x 10^-^3[/tex] ounce, which means that the seed weighs one-thousandth of an ounce.
To write this in standard form, we first convert the number to a decimal between 1 and 10 by moving the decimal point three places to the left. This gives us a decimal of 0.001. The exponent is already in the form of a power of 10, so we can leave it as [tex]10^-^3[/tex]. Thus, the weight of a pitaya seed in standard form is:
[tex]0.001 \times 10^-^3[/tex]
To simplify this expression, we can multiply the decimal and the exponent. This gives us:
[tex]1 x 10^-^6[/tex]
This means that the weight of a single pitaya seed is very small, and it takes many seeds to make up the weight of a whole pitaya fruit.
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PLS HELP! In the figure below, m angle SUT=123 and m arc PR= 124 . Find m arc ST.
The measure of the arc of the circle is mST = 122°
Given data ,
Let the circle be represented as C
where the two chords of the circle are RT and PS
And the chords RT and PS intersect at the point U
Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.
On simplifying , we get
m∠SUT = ( 1/2 ) ( mPR + mST )
123° = ( 1/2 ) ( 124° + mST )
On solving for mST , we get
( 124° + mST ) = 246°
Subtracting 124° on both sides , we get
mST = 122°
Hence , the measure of arc mST = 122°
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A circle with circumference 72π is divided into 10 congruent sectors. Find the area of two sectors. Round to the nearest tenth
A person places $12500 in an investment account earning an annual rate of 8.3%,
compounded continuously. Using the formula V = Pert, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the nearest
cent, in the account after 12 years.
20 POINTS
When a person places $12,500 in an investment account earning an annual rate of 8.3%, compounded continuously, based on the formula V = Pe^rt, the amount of money (future value), to the nearest cent, in the account after 12 years, is $33,842.88.
How the future value is determined:Using the formula A = Pe^rt where V is the future value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.
In this situation, we can use an online finance calculator to determine the future value compounded continuously as follows:
Principal (P): $12,500.00
Annual Rate (R): 8.3%
Compound (n): Compounding Continuously
Time (t in years): 12 years
Result:
A (Future Value) = $33,842.88
A = P + I where
P (principal) = $12,500.00
I (interest) = $21,342.88
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Please help me understand this problem!
The requried solution of the given derivative has been given below.
If F(t) is an antiderivative of t⁵, then we have:
F'(t) = d/dt(F(t)) = t⁵
According to the Second Fundamental Theorem of Calculus, we have:
[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]
Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:
[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]
Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]
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Which best describes the solution set for the compound inequality below?
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
no solution
x = 1
all real numbers except x = 1
all real numbers
The statement that best describes the solution to the inequality in this problem is given as follows:
all real numbers except x = 1.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
The solution to the first inequality is given as follows:
2(x + 7) – 1 > 15
2x + 14 > 16
2x > 2
x > 1.
The solution to the second inequality is given as follows:
3(x + 2) < 2x + 7
3x + 6 < 2x + 7
x < 1.
The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:
all real numbers except x = 1.
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Determine which set of sides measurements could be used of form a right triangle 14,5,15 3,4,5 9,14,16 5,2,7
Answer: 14,5,15 is correct
Step-by-step explanation:
Tres engranajes tangentes entre sí, cuyos radios miden 15, 16 y 17 cm, deben ser sostenidos por
una base triangular que tiene por vértices los centros de cada engranaje. Hallar los ángulos
interiores del triángulo y expresarlos según el sistema de medición radial.
Para resolver este problema, podemos utilizar el Teorema de los Cosenos para calcular los ángulos interiores del triángulo.
Sea A, B y C los vértices del triángulo correspondientes a los centros de los engranajes. Sea a, b y c las longitudes de los lados opuestos a los ángulos A, B y C respectivamente.
Dado que los radios de los engranajes miden 15 cm, 16 cm y 17 cm, podemos considerar que los lados del triángulo son a = 15 cm, b = 16 cm y c = 17 cm.
El Teorema de los Cosenos establece que en un triángulo con lados a, b y c, y ángulos opuestos A, B y C respectivamente, se cumple la siguiente fórmula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Podemos aplicar esta fórmula para cada uno de los ángulos del triángulo.
Para el ángulo A, tenemos:
c^2 = b^2 + a^2 - 2ab * cos(A)
17^2 = 16^2 + 15^2 - 2 * 16 * 15 * cos(A)
Resolviendo la ecuación, encontramos que cos(A) = -1/8. Tomando el coseno inverso (arcocoseno), encontramos que el ángulo A es aproximadamente 135.2 grados en el sistema de medición radial.
Para el ángulo B, tenemos:
a^2 = c^2 + b^2 - 2cb * cos(B)
15^2 = 17^2 + 16^2 - 2 * 17 * 16 * cos(B)
Resolviendo la ecuación, encontramos que cos(B) = -7/17. Tomando el coseno inverso, encontramos que el ángulo B es aproximadamente 120.6 grados en el sistema de medición radial.
Para el ángulo C, tenemos:
b^2 = a^2 + c^2 - 2ac * cos(C)
16^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)
Resolviendo la ecuación, encontramos que cos(C) = -1/2. Tomando el coseno inverso, encontramos que el ángulo C es aproximadamente 120 grados en el sistema de medición radial.
Entonces, los ángulos interiores del triángulo son:
A ≈ 135.2 grados
B ≈ 120.6 grados
C ≈ 120 grados
Estos valores están expresados en el sistema de medición radial.
work out length x in the triangle below
if your answer is a decimal, give it to 1 d.p.
The length x in the triangle below is 16 m.
What is length?Length is the distance between two points.
To calculate the length of the triangle, we use the formula below
Formula:
A = absin∅/2...................... Equation 1Where:
A = Area of the triangle∅ = Included angle of the triangleFrom the question,
Given:
a = 15 mb = x∅ = 30°A = 60 m²Substitute these values into equation 1 and solve for x
60 = (15×x)sin30°/2120 = 15x(1/2)15x = 240x = 240/15x = 16 mLearn more about length here: https://brainly.com/question/28108430
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Be sure to round the mileage to nearest whole mile
The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.For the mileages, we have that:
The slope is the cost per mile.The intercept is the daily cost.Hence the functions are given as follows:
Plan A: A(x) = 30 + 0.14x.Plan B: B(x) = 50.Cost B is the better plan when:
A(x) > B(x)
Hence:
30 + 0.14x > 50
0.14x > 20
x > 20/0.14
x > 142.9 miles -> rounded to 143.
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Eight fourths is proportional to what value?
Eight fourths is proportional to the value of 2/1
What is proportionality of values?Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.
A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.
Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1
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What is the answer to the question please ?
Answer:
Step-by-step explanation:
easy its A tell me if u got it correct good job (:
13. Lindsay was going to visit her grandmother, shop at the mall, and then return home. The route she took was in the shape of a triangle. The distance between each place she visited was 10 miles. What type of triangle is formed by the route she traveled? Explain. answer please answer that question
Can you guys help me with this please
Step-by-step explanation:
Using rules of logs :
9 loga x = loga x^9
Then using another rule:
loga x^9 + loga y = loga (x^9 * y )
You pay for a fiction book, a nonfiction book, and a bookmark with three $5 bills. The fiction book costs $5.43. The nonfiction book costs $3.89. Your change is $3.45. How much does the bookmark cost?
Answer:
2.23
Step-by-step explanation:
You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.
To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.
Here is a map of an island with cities A, B and C Jeremy drives
1) The three figure bearing of B from A when B is due East of A is 090°
2) Note that Kenzi drives 60km further than Jafar.
What is bearing?A) A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.
Hence in the above case of option A, The three figure bearing of B from A when B is due East of A is 090°
B) To find or compute how much further Kenzi drives than Jafar, we need to convert the distances on the map to their real-world distances using the given scale of 1cm to 200km.
So A to B for Jafar -
Distance from A to B = 2.4cm x 200km/ cm = 480km
Then for B to C for Kenzi -
Distance from B to C = (1.2cm + 1.5cm) x 200km/cm
= 2.7cm x 200km/cm
= 540km
So to determine how much further Kenzi drives compared to Jafar
Kenzi drives 540km - Distance from A to B
= 540km - 480 km = 60km
Therefore, Kenzi drives 60km further than Jafar.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
Help me please! I’m really struggling on how to do this
Answer:
12 feet
Step-by-step explanation:
1 inch= 8 feet
1/2 inch= 4 feet
1/4 inch= 2 feet
(2x2)/2= 2 (one triangle)
2x4=8 (rectangle)
2+2=4 +8=12
^2 was added 2 times cause there are 2 triangles
(you did not need a 3rd measurement cause the triangle measurements were equal)
(x+3)(x+7)=0
Problem answered, solution and why!
Answer:
the solution set is { - 7, - 3 }
Step-by-step explanation:
(x + 3)(x + 7) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
x + 7 = 0 ( subtract 7 from both sides )
x = - 7
solution set is { - 7, - 3 }
Please help find the x.
Answer:
The answer is 64°
Step-by-step explanation:
opposite angles are equal
x=64°
Answer:
X is 64 degrees.
Step-by-step explanation:
X is directly across from 64 degrees. These angles are equal. So are angle y and 18, and angle z and the blank angle at the bottom.
Byron worked fewer than 20 days last month. Write an inequality for d, the number of days Byron worked last month.
Answer:
[tex]d < 20[/tex]
Step-by-step explanation:
The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.
One candle, in the shape of a right circular
cylinder, has a height of 7.5 inches and a
diameter of 5 inches. What is the volume of the
candle? Round your answer to the nearest
cubic inch.
Answer:
147
Step-by-step explanation:
V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188
find the perimeter of a triangle where one side is 2 inches, one side is 6 inches and another side is 10 inches.
(a) 2in.
(b) 9in.
(c) 36in.
(d) 18in.
Answer:
(d) 18 in.
Step-by-step explanation:
When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:
P = s1 + s2 + s3, where
P is the perimeter,and s1, s2, and s3 are the three sides:P = 2 + 6 + 10
P = 8 + 10
P = 18
Thus, the perimeter of the triangle is 18 in.
Assessment
What is a brokerage account?
A. An online account used to pay expenses.
B. A deposit account at a financial institution that allows
withdrawals and deposits.
C. An interest-paying deposit account at a financial
institution that provides a modest interest rate.
D. An account used to buy investments like stocks, bonds,
and mutual funds.
5/10
Answer:
Step-by-step explanation:
A brokerage account is an investment account that allows you to buy and sell a variety of investments, such as stocks, bonds, mutual funds, and ETFs.
Therefore the answer is D
Solve. |7x-20|=|2x+20|
To solve the equation |7x - 20| = |2x + 20|, we need to consider two cases based on the absolute values.
Case 1: (7x - 20) = (2x + 20)
Simplifying this equation, we get:
7x - 20 = 2x + 20
Subtracting 2x from both sides:
5x - 20 = 20
Adding 20 to both sides:
5x = 40
Dividing both sides by 5:
x = 8
Case 2: (7x - 20) = -(2x + 20)
Simplifying this equation, we get:
7x - 20 = -2x - 20
Adding 2x to both sides:
9x - 20 = -20
Adding 20 to both sides:
9x = 0
Dividing both sides by 9:
x = 0
Therefore, the solutions to the equation |7x - 20| = |2x + 20| are x = 8 and x = 0.
Instructions: Find the missing probability.
P(B)=1/2P(A|B)=11/25P(AandB)=
If ΔABC is dilated from point A by a scale factor of one half, which of the following equations is true about segment D prime E prime?
segment D prime E prime = one half segment DE
segment D prime E prime = two segment DE
segment D prime E prime = segment DE
segment D prime E prime = three segment DE
An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.
In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:
D'E' = 1/2 × DE
In conclusion, line segment D'E' is equal to one half line segment DE.
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