A student is taking a test. He has 37 questions left. If the test has 78 questions
a. Let x represent the number of questions finished.
b. The equation is x + 37 = 78 , and solving yields x = 41 .
c. The student finished 41 questions.
a. Define a variable for the unknown value. Let x represent the number of questions the student has finished.
b. Write and solve the equation. The total number of questions is the sum of the questions finished and the questions left: x + 37 = 78 . Now solve for x :
x = 78 - 37 = 41
So, the student has finished 41 questions.
c. Answer the question with the correct units. The student has finished 41 questions out of the total 78. Therefore, the student has [tex]\( \frac{41}{78} \)[/tex] of the test complete. To express this as a percentage, multiply by 100:
[tex]\[ \frac{41}{78} \times 100 \approx 52.56\% \][/tex]
The student has finished approximately 52.56% of the test.
Que. A student is taking a test. He has 37 questions left. If the test has 78 questions, how many questions has he finished? a. Define a variable for the unknown value. Let ...........represent............
b. Write and solve the equation.
c. Answer the question with the correct units........
find the missing value in the ratio table .
A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand X aspirin. How many doctors use brand X aspirin? (Hint: Solve for X
Hey guys, I need help answering this question for my Algebra 2 class.
How many 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times?
30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
What is Number system?A number system is defined as a system of writing to express numbers.
By means of Permutation we solve this
The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
The formula for permutation is [tex]^{n}P_{r} =\frac{n!}{(n-r)!}[/tex]
n is total number of objects
r is number of objects selected
We need to find 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
¹⁰P₅=10!/(10-5)!
=10!/5!
=10×9×8×7×6×5!/5!
=30240
Hence, 30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
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subtract the fractions and simplify the answer 7 8/9-5 3/5
To subtract the fractions 7 8/9 and 5 3/5, first convert them into improper fractions. Then, adjust them to the common denominator (45 in this case) and subtract to get the answer of 2 13/45.
Explanation:To begin, we need to convert these mixed fractions (7 8/9 and 5 3/5) into improper fractions. 7 8/9 equals 71/9 (since 7*9 + 8 = 71) and 5 3/5 equals 28/5 (since 5*5 + 3 = 28). Now, we can subtract these fractions by finding a common denominator or a number that 9 and 5 mutually divide into. This number is 45. Therefore, we adjust these fractions to have the denominator of 45, getting 355/45 and 252/45. The subtraction of these adjusted fractions equals 103/45. That can be simplified into 2 13/45.
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You are 5 feet tall and cast an 8-foot shadow. A lamppost nearby casts a shadow that is 20 feet. Which equation can you use to solve for the height (h) of the lamppost?
A. 5/8 = h/20
B. 8/5= h/20
C. 5/9 = h/20
D. 5/20 = h/8
Answer:
A. 5/8 = h/20
Step-by-step explanation:
Topic: Triangle Similarity
As you can see in the image you can paint the problem that way, it means that each side of the triangle is a multiplier from the other one same side, so you can build a relation as follows:
[tex]\frac{5}{h} = \frac{8}{20} \\[/tex]
you can re arrange the equality as
[tex]\frac{5}{8} = \frac{h}{20}[/tex]
as you can ssee you just reached the option A. 5/8 = h/20
a skirt that usually sells for $40 is on sale for $30. What is the discount percent?
A) 20%
B) 25%
C) 27%
D) 30%
In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve? A) 10 B) 15 C) 25 D) 35
Answer:
B) 15
Step-by-step explanation:
In order to solve this we have to create a system of equations, where the easy puzzles are represented by x, and the hard puzzles are y, so you just have to multiply that for the points to get the total points in all:
30x+60y=1950
If the player did 50 in total:
x+y=50
Now we just solve for x in the second equation and then insert that into the first equation:
x=50-y
30(50-y)+60y=1950
1500-30y+60y=1950
30y=450
y=450/30
y=15
So we know that Tina solved 15 hard puzzles.
6× 532 expanded form
What is 27 multiplied by 36 worked out?
If the variance of a probability was computed to be 3.6 grams, what is the standard deviation
The standard deviation is the square root of the variance, which is about 1.897 grams when the variance is 3.6 grams.
Explanation:If the variance of a probability was computed to be 3.6 grams, the standard deviation is the square root of the variance. To calculate the standard deviation, you perform the following steps:
First, recognize that variance (σ²) is the square of the standard deviation (σ).To find the standard deviation, take the square root of the variance.Therefore, the standard deviation is √3.6 g.By using a calculator, we find that the standard deviation is approximately 1.897 grams.
Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10.
A. –10 < |3x – 5| < 10
B. 3x – 5 > –10 or 3x – 5 < 10
C. 3x – 5 < –10 or 3x – 5 > 10
D. –10 < 3x – 5 < 10
Compound inequality is the combination of more than one inequality.
The compound inequality from [tex]|3x - 5| > 10[/tex] is:
(c) [tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]
Given that:
[tex]|3x - 5| > 10[/tex]
When the above inequality is split, we have the following inequalities:
[tex]3x - 5 > 10[/tex]. [tex]3x - 5 < -10[/tex]So, the result of the split is:
[tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]
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An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
What must the distance be between charges of +2.35 and −1.96 for the attractive force between them to be the same as that between charges of +4.06 and −2.11 separated by a distance of 2.26 pm?
The distance between charges of +2.35 and −1.96, should be approximately 1.566 picometers (pm).
Coulomb's law states that the force (F) between two point charges is given by:
F =[tex]\dfrac{(k \times q1 \times q2)}{r^2}[/tex]
Where:
The electrostatic force between the charges is F
k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C².
The magnitudes of the two charges are [tex]q_1[/tex] and [tex]q_2[/tex].
The distance between the charges is r.
Given that the charges are +2.35 and −1.96, we'll call the distance between them x (in pm). Similarly, for charges +4.06 and −2.11, the distance is given as 2.26 pm.
Setting up the equation:
For the first pair of charges (q1 = +2.35 C and q2 = −1.96 C):
F1 =[tex]\dfrac{(k \times |2.35 \times (-1.96)|)}{x^2}[/tex]
For the second pair of charges (q1 = +4.06 C and q2 = −2.11 C):
F2 =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]
Since the forces are said to be equal, we have:
F1 = F2
The solution of the expression for x is given by:
[tex]\dfrac{(k \times |2.35 \times (-1.96)|}{x^2}[/tex] =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]
|[tex]\dfrac{(2.35 \times (-1.96)}{x^2}[/tex]| =[tex]\dfrac{|4.06 \times (-2.11)|}{ (2.26)^2}[/tex]
[tex]{(2.35 \times 1.96)} {x^2}[/tex] = [tex]\dfrac{(4.06 \times 2.11)} { (2.26)^2}[/tex]
[tex]x^2[/tex] =[tex]\dfrac{(2.35 \times 1.96 \times (2.26)^2} {(4.06 \times 2.11)}[/tex]
[tex]x^2[/tex] = 2.450206485
x ≈ [tex]\sqrt{2.450206485[/tex]
x ≈ 1.566 pm
Therefore, the distance between charges of +2.35 and −1.96, should be approximately 1.566 picometers (pm).
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To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same, use Coulomb's Law to calculate the force between charges of +4.06 and -2.11 separated by a distance of 2.26 pm. Then solve for the distance using the same formula and the calculated force value.
Explanation:To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same as between charges of +4.06 and -2.11, we can use Coulomb's Law. The formula for calculating the force between two charges is F = k * (|q1 * q2| / (d^2)) where k is the proportionality constant and d is the distance between the charges.
First, we calculate the force between charges of +4.06 and -2.11. Let q1 = +4.06, q2 = -2.11, and d = 2.26 pm. Plugging these values into the formula, we get:
F = (1/47e) * (|4.06 * -2.11| / (2.26^2))
Next, we can find the distance between charges of +2.35 and -1.96 such that the attractive force is the same. Let q1 = +2.35, q2 = -1.96, and F = the value we calculated earlier. Rearranging the formula to solve for d, we get:
d = sqrt((|q1 * q2| / (F * k)))
1 and 2/5(-3/5) in simplest form
Set up a proportion for the problem below:
15 is 1 1/2% of what number?
Please answer ASAP!! Thank you :)
3m-5m-12=7m-88-5
plz show all work
Suppose w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t).
a. use the chain rule to find dwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2t as x.
Final answer:
To find dwdt using the chain rule, differentiate w=xy+yz, where x=e^2t, y=2+sin(4t), and z=2+cos(7t), as functions of t, apply partial derivatives and multiply by dx/dt, dy/dt, and dz/dt.
Explanation:
The student asked how to use the chain rule to find dwdt as a function of x, y, z, and t, without rewriting x, y, and z in terms of t, and keeping e2t as x. Given w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t), we apply the chain rule to differentiate w for t, remembering that x, y, and z are all functions of t. To find debt, we derive each component individually and sum their contributions. The calculation involves taking partial derivatives of w to x, y, z, multiplied by their respective derivatives to t (dx/dt, dy/dt, dz/dt).
Manuel stores his favorite CDs in a box like the one shown
Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true?
A) In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.
B) In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.
C) In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.
D) In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
The statements that are true about the information given will be:
In Euclidian geometry, the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.It should be noted that Euclidian geometry is simply about understanding the geometry of flat, two-dimensional spaces while non-Euclidian geometry is about curved surfaces.
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Find f '(−5), if f(x) = (−4x2 − 2x)(−x2 − 9)
Answer: the answer is -2192
How do I solve 9a-7=110
Convert 4 fluid ounces of soap per quart of water to cups of soap per gallon of water.
which of the following is a correct interpretation of the expression -2+(-7)
The correct interpretation of -2 + (-7) is that "the number 7 is to the left of -2 on the number line".
The correct interpretation of the expression -2 + (-7) which is results in -9.
Let's break this down:
-2 is our starting point on the number line. + (-7) means we move 7 units to the left of -2 (since adding a negative number is equivalent to subtraction).When we move 7 units left from -2, we land on -9.
Thus, -2 + (-7) results in -9, which confirms that we have moved 7 to the left of -2 on the number line.
Complete question:
Which of the following is a correct interpretation of the expression -2 + (-7)?
Choose 1 answer:
The number that is 2 to the left of 7 on the number lineThe number that is 2 to the right of 7 on the number lineThe number that is 7 to the left of −2 on the number lineThe number that is 7 to the right of −2 on the number lineThe length of a rectangle is three times its width. If the area of the rectangle is 192 ft^2, find its perimeter
The picture shows a triangular island Which expression shows the value of Q?
S/cos 55• the answer D
The perimeter of a rectangular field is 264 yards. If the width of the field is 54 yards, what is its length?
HURRY
At the grocery store checkout, you watch at the register as it rings up your purchases and coupons. The prices are as follows: $2.95 $1.19 $4.61 $1.74 $3.04 $8.83 $1.16 − $0.75 (coupon) − $1.00 (coupon) The register gives your total bill as $21.77. Round each price and coupon to the nearest dollar and then estimate the total amount of the bill. Using your estimate, determine whether the total on the register is reasonable. Justify your answer.
How to find the sum of the forces in the y direction of an elevator?
The way to calculate the sum of the forces in the y direction of an elevator; has been outlined below
Equilibrium of Forces
If you are in an elevator by itself, then the combined system of you and the elevator could have 3 possible situations which are;
The elevator has no acceleration because it is standing still or moving with constant velocity.The elevator has an upward acceleration because it is accelerating upward, or decelerating while it's way down.The elevator has a downward acceleration since it is accelerating down, or decelerating while on the way up.Now, in the vertical y direction, there are three forces namely;
The force of gravity.A downward normal force.An upward force from the tension in the cable holding the elevator.Thus, the sum of forces in the y-direction with the normal force acting on you from the elevator are any of the following;
N = mg; provided that the elevator is at rest or moving at constant velocity.
N = mg + ma; Provided that the elevator has an upward acceleration.
N = mg - ma; Provided that the elevator has a downward acceleration.
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In an elevator at rest, the sum of the forces in the y direction is equal to the weight of the person.
Explanation:If the elevator is at rest, the sum of the forces in the y direction is equal to zero. This means that the upward force exerted by the scale, Fs, must be equal to the downward force exerted by the weight of the person, w. According to Newton's third law, Fs and Fp (the force exerted by the person on the scale) are equal in magnitude and opposite in direction.
To find the value of Fs, we can apply Newton's second law, which states that the net force in the y direction is equal to the mass of the object times its acceleration. In this case, the net force is Fs - w and the acceleration is zero. Therefore, Fs = w.
So, the sum of the forces in the y direction of the elevator is equal to the weight of the person.