Answer:
See below.
Step-by-step explanation:
a. 973 * 80
= 973 * 8 * 10
= 7784 * 10
= 77,840.
b. 56 * 2000
= 2*56 * 1000
= 112,000.
c. 5.7 * 300
= 5.7 * 3 * 100
= 17.1 * 100
= 1710.
d. 0.46 * 50
= (0.46 * 100) / 2
= 46 / 2
= 23.
Answer with Step-by-step explanation:
a. 973 × 80
= 973 × 8 × 10
= 7784 × 10
=77840
b. 56 × 2,000
=56 × 2 × 1000
=112 × 1000
=112000
c. 5.7 × 300
=5.7 × 3 × 100
=17.1 × 100
=1710
d. 0.46 × 50
=0.46 × 5 × 10
=2.3 × 10
=23
Peter calculated that the theoretical probability of obtaining exactly two heads when flipping six coins is 23.4%. What number of heads also has a 23.4% theoretical probability of coming up when 6 coins are flipped?
Answer:
4 heads
Step-by-step explanation:
Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.
If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.
Which expressions represent 1 more then the product 5 and 2
Answer:
1+5*2 or simplified, 1+10= 11
what is the domain of the function in this table? X 3 4 5 6 Y 4 4 2 5
Answer:
The domain is {3,4,5,6}
Step-by-step explanation:
Because all your x - values is ur domain and ur y - values is ur range
I AM GIVING 10 POINTS TO WHOMEVER ANSWERS THIS!!!
Simplify: 9^-5 × 9^-3
A) 1/9^8
B) 1/9^2
C) 9^8
D) 9^15
Answer:
A) (1/9)^8
Step-by-step explanation:
9^-5 × 9^-3 =
Rule: a^m * a^n = a^(m + n)
= 9^-8
Rule: (a^m)^n = a^(mn)
= (9^-1)^8
Rule: a^-m = 1/a^m
= (1/9)^8
Answer: A) (1/9)^8
Write the quadratic equation whose roots are 6 and -5, and whose leading coefficient is 3
To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.
Explanation:The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5).
Expanding this, we have:
3(x² + 5x - 6x - 30)3(x² - x - 30)3x² - 3x - 90The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.
The area of a rectangle is 27 square meters. If the length is 6 meters less than 3 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth
Answer:
width = 4.16 meter
length = 6.49 meter
Step-by-step explanation:
Area of the rectangle =27 m²
Let the width of the rectangle be x meter
So, Length = 3 * width - 6
= 3*x - 6
= 3x-6 meter
Area of the rectangle = length * width
27 = (3x-6)*x
Flipping the sides of the equation, we have
(3x-6)*x =27
Distributing the left side, we get
(3x)*(x) - (6)*(x) = 27
=> 3x² - 6x = 27
Subtract 27 from both sides,
3x² - 6x -27 = 27 - 27
=> 3x² - 6x -27 = 0
Factoring out 3 from all the terms on the left side, we have
3(x² - 2x -9) = 0
Dividing both sides by 3, we have
[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]
Cancelling out the 3's on the left, we get
x² - 2x -9 = 0
We'll use the quadratic formula to solve for the x,
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get
a = 1 (as x² has no coefficient)
b = -2
c = -9
Plugging in the values of a, b, and c into the quadratic formula, we get
x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]
=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]
=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]
=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]
Factoring out 2 from the top, we get
x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]
Canceling out the 2's from the top and bottom, we have
x = [tex]1\pm\sqrt{10}[/tex]
Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]
=> x = 1 + 3.162 or x = 1 - 3.162
=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)
So, width = 4.16 meter (rounded off to the nearest hundredth)
Now,
Area of the rectangle = length * width
27 = length * 4.16
Flipping the sides of the equation,
length * 4.16 = 27
Dividing both sides by 4.16, we get
[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]
Cancelling out 4.16 from the top and bottom of the left side, we get
length = 6.490
=> length = 6.49 meter (rounded off to the nearest hundredth)
PLEASE HELP ASAP! I don’t know how to do this can someone please help.
Answer: 2.50
Step-by-step explanation: your answer is 2.50
Which of the following expression is equal to 6-4(x+3)?
Answer:
-3
Step-by-step explanation:
6-4 (x+3)
2(x+3)
2x+6=0
2x=-6
2x/2= -6/2
x=-3
A football team lost 3 yards on the first play in 6 yards on their second play. How many total yards did they lose?
Answer:-11
Step-by-step explanation:
use -6 to represent losing 6 yards
use -5 to represent losing 5 yards
add these together
(-6) + (-5) = -11
when adding two negative values, make sure your sum is negative
Answer:
it is 9
Step-by-step explanation:
6 plus 3 is 9
I had this for homework so I know
You had 15 text messages, deleted 2 then got 5 more, you responded to 4,
and whats your total? a, b, or c?
A. 12
B. 14
C. 18
Answer: The answer is C
Step-by-step explanation: 15 - 2 = 13 13+5=18
Hope this helps :)
What is 25% of $1200?
A) 900
B) 250
C) 600
D) 300
Answer:
The answer Is D
Step-by-step explanation: I looked it up on Google, next time just type it into Google because it will solve it on a calculator for you.
Answer: It is choice D
Step-by-step explanation: To figure out 25% of 1,200, multiply 1,200 by 0.25. 1,200 x 0.25 = 300
Find the equation of the circle with center at (3, 2) and through the point (5, 4).
Answer:
(x - 3)² + (y - 2)² = 8
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre to a point on the circle
To find r use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁)²
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)
r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]
(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²
(x - 3)² + (y - 2)² = 8 ← equation of circle
please help???????????
Answer:
x - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
A polynomial has the form
first term is the term of highest degree followed by term of second etc.
note that x = [tex]x^{1}[/tex] ← degree 1
x - [tex]\sqrt{7}[/tex]
fits this description and is a polynomial of degree 1
You will be Brainiest Answered if answered.
Thanx
Answer:
9R30
Step-by-step explanation:
9
36)354
324
30
What is the coefficient of q in the sum of these two expressions? (23q – 34) and (–16q – r) NEED HELPPP
The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.
Explanation:In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.
The sum of the two expressions is (23q - 34) + (-16q - r).
To find the coefficient of q in this sum, we need to combine the like terms.
Combining the q terms, we have 23q - 16q = 7q.
Therefore, the coefficient of q in the sum of the two expressions is 7.
Can you help me to determine the y-intercept of 7 and slope please
Answer:
slope = 2.5 and the y intercept is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/(x2-x1)
I will use the point (2,8) (6,18) We can pick any 2 point we want.
= (18-8)/(6-2)
= (10/4)
= 2.5
To find the y intercept we need to find the equation of the line.
We will use the point slope form
y-y1= m(x-x1)
y-8 = 2.5(x-2)
Distribute the 2.5
y-8 = 2.5x-5
Add 8 to each side
y-8+8 = 2.5x-5+8
y = 2.5x+3
This equation is in slope intercept form y = mx+b
where the slope is 2.5 and the y intercept is 3
Hi There!
-----------------------------------
Find The Slope:
[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]
-----------------------------------
Find The Y-Intercept:
Substitute using x = 2 and y = 8
Use y = mx + b
Substitute: 8 = 2.5(2) + b
Simplify: 8 = 5 + b
Subtract 5 too both sides: 8 - 5 = 5 + b - 5
Simplify: 3 = b
Y-Intercept = 3
-----------------------------------
Point Slope Form: y - 8 = 2.5(x - 2)
Slope Intercept Form: y = 2.5x + 3
-----------------------------------
Hope This Helps :)
George spun a 6 sided spinner that had colors blue, red, white, yellow, black, and purple. She landed on blue-3 times, red-4-times, white-3 times, yellow-2 times, black-5 times, and purple-1 time. What is the experimental probability that George will spin a red then a yellow?
Answer:
[tex]\frac{2}{81}[/tex]
Step-by-step explanation:
Step 1
List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18
Step 2
The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,
[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]
The correct answer is [tex]\frac{2}{81}[/tex]
Together, teammates Pedro and Ricky got 2677 base hits last season. Pedro had 275 more hits than Ricky. How many hits did each player have?
Answer:
Ricky = 1201
Pedro = 1476
Step-by-step explanation:
Assign variables
let p be the number of Pedro's base hits
let r be the number of Ricky's base hits
Create a system of equations
p + r = 2677 <= Pedro and Ricky got 2677 base hits
p = r + 275 <= Pedro had 275 more hits than Ricky
Solve using the substitution method (replace a variable with an expression)
p + r = 2677
Substitute "p" with "r + 275"
r + 275 + r = 2677
Combine like terms to simplify
2r + 275 = 2677
Isolate "r" by moving everything else to the right side.
2r = 2677 - 275 Subtract 275 from both sides
2r = 2402
2r/2 = 2402/2 Divide both sides by 2
r = 1201 Ricky's base hits
To find Pedro's hits, substitute "r" into any equation.
p = r + 275
p = 1201 + 275 Substitute r = 1201, then add
p = 1476 Pedro's base hits
∴ Ricky had 1201 base hits and Pedro had 1476 base hits.
Final answer:
By setting up an equation where R represents Ricky's hits, and calculating R + 275 for Pedro's hits, we can solve for R and then find the number of hits for each player. Ricky had 1201 hits, while Pedro had 1476 hits.
Explanation:
To solve the problem of determining how many base hits Pedro and Ricky each had last season, we can use algebra. Let's let the variable R represent the number of hits Ricky had. Since Pedro had 275 more hits than Ricky, we can express Pedro's number of hits as R + 275. According to the question, the sum of their hits is 2677, so the equation will be R + (R + 275) = 2677.
Now, let's solve the equation:
R + R + 275 = 2677
2R + 275 = 2677
2R = 2677 - 275
2R = 2402
R = 2402 / 2
R = 1201
So, Ricky had 1201 hits. To find Pedro's hits, we substitute R into the expression R + 275:
Pedro's hits = R + 275 = 1201 + 275 = 1476
Therefore, Ricky had 1201 hits and Pedro had 1476 hits.
the legs of a isosceles right triangle both measures 10 inches find the lenth of the hypotenuse
Answer:
Step-by-step explanation:
You just add and subtract
each roll of tape is 30.5 feet long. a box contains 454 rolls of tape. in total, there are _ yards
Answer:
4617 yd
Step-by-step explanation:
30.5 ft make 1 roll of tape
Length of tape = 454 × 30.5/1
Length of tape = 13 847 ft
1 ft = 3 yd
Length of tape = 13 847 × 1/3
Length of tape = 4617 yd
A publishing company is going to have 24,000 books printed. There are between 3 and 4 books out of ever 3,000 that will have a printing error. At this rate, which number could be the exact number of books that will have a printing error? a. 7 b. 12 c. 31 d. 36
Answer:
C. 31
Step-by-step explanation:
3000 there are 3-4 errors
If we first divide 24,000 by 3,000, will get 8
then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24
32 (8 x 4) the max amount of printing errors
24 (8 x 3) the minimum amount of printing errors
So we should expect 24-32 printing errors
Only answer between the numbers is c. 31
Final answer:
The exact number of books that could have a printing error out of 24,000, given the rate of 3 to 4 errors per 3,000 books, can be calculated to be within a range, making 31 the only viable option provided.
Explanation:
The question is about determining the exact number of books that will have a printing error out of 24,000, given that there are between 3 and 4 printing errors per every 3,000 books. To find the possible number of errors, we multiply the number of books (24,000) by the rate of errors (3 to 4 per 3,000). This gives us a range of possible errors, from (24,000 / 3,000) * 3 = 24 to (24,000 / 3,000) * 4 = 32. Therefore, the only option within this range is 31.
Tess left her home and drove for 3.7 hours due north at a rate of 60 miles per hour. After attending a concert, she drove due south for 1.4 hours at 55 miles per hour.
How far is Tess from her home?
Answer: 145
3.7 x 60 = 222 (how far north she drove)
1.4 x 55 = 77 (how far south she drove)
222 - 77 = 145 (how far from home)
325 Students and adult Will be riding the buses .Each buses hold 48 people.how many buses are needed .
Answer:
7 buses are needed.
Step-by-step explanation:
There are 325 students and adults.
Each bus holds 48 people.
The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333
Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;
325 - (48 × 6) = 37 people will not fill the last bus.
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies. Nonmembers pay $3 for new release movies. Write a system of linear equations that represents this situation
Answer:
The system of linear equations are
y = 15 + 2x
y = 3x
Step-by-step explanation:
Let us assume that the number of new release movies be x.
Let us assume that the total cost be y.
As given
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.
Than the equation becomes
y = 15 + 2x
As given
Nonmembers pay $3 for new release movies.
y = 3x
Therefore the system of linear equations are
y = 15 + 2x
y = 3x
Are the solutions correct?
Answer:
First one is wrong. x should be 16.
Second one is not completely visible, so cannot say.
Step-by-step explanation:
In the last step, the divison by 4 yields:
x/16 = 1, so x = 16
a maximum speed, and airplane travels 2460 miles against the wind in 6 hours. flying with the wind, the plane can travel the same distance in 5 hours
Answer:
for pluto answer is 451
Step-by-step explanation:
find the unit rate off $1.29 for 3pens
Answer:
$.43 per pen
Step-by-step explanation:
To find the unit rate, we take the price of the pens and divide by the number of pens
$1.29/3
$.43 per pen
Answer: $0.43
Step-by-step explanation:
Unit rate is how much each pen costs.
If the total amount is $1.29 for all three pens, then the price for one pen should be calculated by 1.29/3, therefore, the answer is $0.43
3/7-2/14 (8-1/2) +2/7
What is the vertex form of the quadratic y = 3x^2 + 18x - 4?
Answer:
y = 3(x + 3)² - 31
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
take out a common factor of 3 from the first 2 terms
y = 3(x² + 6x) - 4
add/subtract ( half the coefficient of the x-term)² to x² + 6x
y = 3(x² + 2(3)x + 9 - 9 ) - 4
y = 3(x + 3)² - 27 - 4
y = 3(x + 3)² - 31 ← in vertex form
Match the following reasons with the statement givem
Answer:
AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent
In triangle RAS and triangle QAT
[tex]\angle R =\angle Q[/tex] [Angle]
[tex]AS =AT[/tex] [Side] [Given]
By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.
⇒ [tex]\angle 5= \angle 6[/tex] [By base ∠'s of isosceles triangle are equal]
By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.
[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.
⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and
[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]
Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]
[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]
Since, [tex]\angle 5 =\angle 6[/tex]
then, we get;
[tex]\angle 4 =\angle 7[/tex] [Angle]
then, by AAS postulates,
[tex]\triangle RAS \cong \triangle QAT[/tex]
By CPCT[Corresponding Part of Congruent Triangles are equal]
[tex]RS = QT[/tex] Hence Proved!