Note: Consider we need to find each type of coins he has.
Given:
Erin has quarters and nickels for a total of 16 coins.
The value of his coins is $2.60.
To find:
The number of each type of coins.
Solution:
Let x represent the number of quarters and y represent the number of nickels.
According to the question,
Total coins : [tex]x+y=16[/tex] ...(i)
Total value : [tex]0.25x+0.05y=2.60[/tex] ...(ii)
Multiply equation (i) by 0.25 and subtract the result from (ii).
[tex]0.25x+0.05y-0.25(x+y)=2.60-0.25(16)[/tex]
[tex]0.25x+0.05y-0.25x-0.25y=2.60-4[/tex]
[tex]-0.20y=-1.40[/tex]
Divide both sides by -0.20.
[tex]y=7[/tex]
Put y=7 in (i).
[tex]x+7=16[/tex]
[tex]x=16-7[/tex]
[tex]x=9[/tex]
Therefore, the number of quarters is 9 and number of nickels is 7.
What is the answer for 5x1+2?
I
Answer:
7
Step-by-step explanation:
A:
Using this figure,
B' is the
of B.
reflection
prelmage
dilation
Image
Answer:
reflection
Step-by-step explanation:
The correct answer would actually be image... if you need to choose more than one option it could additionally be one of the other options but without a figure it's impossible to tell.
It is known that a particular laboratory task takes the average person 2.5 seconds (the variance is not known). A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude?
Complete Question
It is known that a particular laboratory task takes the average person 2.5 seconds (the variance is not known). A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude? (Use the .05 significance level and use the five steps of hypothesis testing.)
Answer:
The researchers conclusion is
There is no sufficient evidence to show that older people are slower at the laboratory task
Step-by-step explanation:
From the question we are told that
The mean time is [tex]\mu = 2.5 \ seconds[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 2.7 \ seconds[/tex]
The standard deviation is [tex]\sigma = 1.4 \ seconds[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 2.5[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2.5[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{2.7 - 3 }{ \frac{1.4}{\sqrt{30} } }[/tex]
=> [tex]z =0.78[/tex]
From the z table the area under the normal curve to the right corresponding to [tex]z =0.78[/tex] is
[tex]p-value = P(Z > 0.78) = 0.2177[/tex]
From the value obtained we see that the p-value > [tex]\alpha[/tex]
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the older people are slower at the laboratory task
A ball was thrown up into the air and allowed to bounce until it came to a halt.
10 +
9
8
N
6
Height in Feet
4
3
m
2.
1
o
0
1 2 3 4 5 6 7 8 9 10
Time in Seconds
At which of the following intervals did the height of the ball increase and then decrease?
0 0 SXS4
25x54
Ο ΟΟΟ
5 SXS7
75x59
In the interval 0 ≤ x ≤ 4 the height of the ball increase and then decrease option (A) is correct.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that:
The ball was thrown up into the air and allowed to bounce until it came to a halt.
As we know,
The parabola can be defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the :
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
Thus, in the interval 0 ≤ x ≤ 4 the height of the ball increase and then decrease option (A) is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ2
Work out please what is it
Step-by-step explanation:
a.5/7
b.12/8= 6/4 = 3=2 =
1 and 1/3
c. 4/6-3/6=
1/6
Answer:
a.)5/7
b.)1.5 or 1 1/2
c.)1/6
Step-by-step explanation:
Determine the unknown angle measure for each triangle. PLS HELP I DONT GET IT LOL IF YOU HELP ME YOULL GET BRAINLIEST PLSSS ASAP
Answer:
Step-by-step explanation:
Hi there.
1a. m C= 44 degrees
46+90= 136 180-136=44
1b. m P= 60 degrees
10+110=120 180-120=60
For future reference, you can solve these with some simple addition. The sum of the angles in any triangle is 180, so add your two given pieces together and subtract it from that to get your missing measure.
2a. Lines a and b have a positive slope. You can tell because they are tilted to the right.
2b. Line d has a negative slope. It's tilted to the left.
(Line c's slope is neither positive or negative because it is zero)
3. x= 65
(I'm not so sure about this one, but I think the angle opposite 25 is also 25, and because of parallel rules the angle above 70 is 110. That means the angle above 110, inside the triangle, is 90. So, we have 90 and 25 and that means 65 is our remaining measure. I really hope this is correct. If you have some sort of notes sheet on the rules of parallel lines and their angle measures, that might be helpful)
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Playing a game of roulette, where the wheel consists of slots numbered
00,0,1,2,...,48
To play the game, a metal ball is spun around the wheel and is allowed to fall
into one of the numbered slots.
Identify the sample space.
A). the sample space is (00,0)
B). the sample space is (00).
C). the sample space is (1,2,...,48)
D). the sample space is (00,0,1,2,...,48)
Answer:
D
Step-by-step explanation:
Marcus spent 3.25$ to wash his car. If one querter operates the car wash 60 seconds hiw long did it take him to wash his car.
10 min or 13 min. or 16 min ir 32.5 min
Answer:
answer=answer
Step-by-step explanation:
Y E S
I love simple math.
3.25$ to wash the car.
60 seconds: 1 quarter
how many quarters is 3.25?
4 quarters per dollar. so it'd be 13 quarters, then do 13*60=how many seconds u got. 780 seconds. I think you can do 780/60
HINT: hey, psst, it's 13 minutes. : D
HEY DOn'T teLL tHeM tHe ANSWER. :V
which ones are arithmetic or geometric ?
(GIVING BRAINLIEST ON THIS ONE!!)
Solve six and two sixths times one and one half.
A) eight and six twelfths
B) nine and six twelfths
C) ten and two twelfths
Answer:
B
Step-by-step explanation:
6 2/6 x 1 1/2
(6 x 6) + 2 = 38/6
(1 x 2) + 1 = 3/2
38/6 x 3/2 = 114/12.
114 ÷ 12 = 9 6/12
9 6/12 = 9 3/6 = 9 1/2.
B
Answer:
the answer is b) nine and six twelfths
Step-by-step explanation:
hoped that helped
Please answer see the image
Answer:
39 km²Step-by-step explanation:
surface area of a square pyramid
= Area of base + 1/2 base perimeter * slant height
= (3 x 3) + (1/2 x (3*4) x 5)
= 9 + 30
= 39 km²
5x-6y=-4
-6x+6y=-6
solve using elimination
HELP.
Answer:
x=10 y=9
Step-by-step explanation:
answer asap..........
Answer:
Quadrant I: (⅓, 2⅓)
Quadrant II: (-1⅓, 3⅓)
Quadrant III: (-3, -10) (-3⅓, -1⅓)
Quadrant IV: (9, -1)
Step-by-step explanation:
If it is (+, +), it is in quadrant I.
If it is (-, +), it is in quadrant II.
If it is (-, -), it is in quadrant III.
If it is (+, -), it is in quadrant IV.
A minor league baseball park has 6800 seats. Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200. If the number of bleacher seats is 2 times the number of box seats, how many seats of each type are there?Box seats:_______ Grandstand seats:_______ Bleacher seats:______
Answer:
Step-by-step explanation:
Let us represent
The number of Box seats = x
The number of grandstand seats = y
The number of bleacher seats cost = z
A minor league baseball park has 6800 seats.
Hence,
x + y + z = 6800
Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200.
Hence:
$19 × x + $9 × y + $4 × z = $61200
19x + 9y + 4 z = 61200
If the number of bleacher seats is 2 times the number of box seats
z = 2x
Hence we substitute
x + y + z = 6800
x + y + 2x = 6800
3x + y = 6800.... Equation 3
y = 6800 - 3x
For Equation 2, substituting 2x for z
19x + 9y + 4z = 61200
19x + 9y + 4(2x) = 61200
19x + 9y + 8x = 61200
27x + 9y = 61200...... Equation 4
Combining Equation 3 and 4
3x + y = 6800.... Equation 3
27x + 9y = 61200...... Equation 4
Note that:
y = 6800 - 3x
We substitute the above in Equation 4
27x + 9(6800 - 3x) = 61200
27x + 61200 - 27x = 61200
Box seats:_______ Grandstand seats:_______ Bleacher seats:______
As Sally was shopping for a turkey tree for Thanksgiving, she looked at 48 trees. Of those, she found that 7/8 of them were too small. How many of the trees were too small?
Answer:
42 treesStep-by-step explanation:
48/1 x 7/8 = 6/1 x 7/1 (Simplify 48 and 8 because they have the common factor of 8)=42/1= 42Answer:
Forty-two (42) of the trees were too small.
Step-by-step explanation:
Find 7/8 of 48.
[tex]\frac{7}{8}[/tex] = 0.875
Multiply the quotient (0.875) by 48 to find [tex]\frac{7}{8}[/tex] of 48.
0.875 × 48 = 42
how do you solve 4x+10=3x+37
Answer:
x = 27
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Equality PropertiesStep-by-step explanation:
Step 1: Define equation
4x + 10 = 3x + 37
Step 2: Solve for x
Subtract 3x on both sides: x + 10 = 37Subtract 10 on both sides: x = 27Step 3: Check
Plug in x to verify it's a solution.
Substitute: 4(27) + 10 = 3(27) + 37Multiply: 108 + 10 = 81 + 37Add: 118 = 118And we have our final answer!
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was en pty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute. Let x be the number of minutes water has been added. Write an equation to show when the two pools would have the same amount of water. You do NOT need to solve this.
Answer:
52 minutes
Step-by-step explanation:
Equation:
[tex]728+23x=0+37x\\728+23x=37x\\728=14x\\x=52[/tex]
So 52 minutes.
Hope this helps plz hit the crown :D
Probability gender of one child
Answer:
about 50% of a girl and 50% of a boy
Step-by-step explanation:
I hope this helps
Is (10,8) a solution of y =1/2x+3
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
1/2=.5 and .5x10=5, 5+3=8 so that proves it is correct.
What number will you get the same result if you multiply it by 3 and add 1, OR if you multiply it by 2 and add 8?
Answer:
7
Step-by-step explanation:
3×7+1=22
2×7+8=22
Two complex numbers have a product of 30 and positive integers as real parts. Write all possible combinations of such numbers.
Answer:
[tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex], [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex], [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex],
[tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex], and [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex].
Step-by-step explanation:
Given that two complex numbers have a product of 30 and the real part of the complex numbers are positive integers.
Let one complex number is [tex]a+ib[/tex] where [tex]a[/tex] is a positive integer and [tex]b[/tex] is a real number.
As the product of two complex numbers is a purely real number, so the other complex number must be the conjugate of the first complex number.
So, another complex number [tex]= a-ib[/tex]
As a product of both the numbers = 30
[tex]\Rightarrow (a+ib)(a-ib)=30 \\\\\Rightarroe a^2 - (ib)^2=30 \\\\\Rightarrow a^2 - (i^2b^2)=30 \\\\Rightarrow a^2 - (-1\times b^2)= 30[/tex] [as i^2=-1]
[tex]\Rightarrow a^2+b^2= 30 \\\\\Rightarrow b^2 = 30-a^2 \\\\[/tex]
[tex]\Rightarrow b=\pm \sqrt {30-a^2} \cdots(i)[/tex]
Now, as a is a positive integer, so by taking possible values of a, we can determine the values of b from the equation (i).
For [tex]a=1[/tex]
[tex]b=\pm \sqrt {30-1^2}=\pm \sqrt {29}[/tex]
The positive sign is for the one number and the negative sign is for the conjugate number (another number).
So, the 1st combination is [tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex]
Similarly,
For [tex]a=2[/tex]
[tex]b=\pm \sqrt {30-2^2}=\pm \sqrt {26}[/tex]
So, the 2nd combination is [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex]
For [tex]a=3[/tex]
[tex]b=\pm \sqrt {30-3^2}=\pm \sqrt {21}[/tex]
So, the 3rd combination is [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex]
For [tex]a=4[/tex]
[tex]b=\pm \sqrt {30-4^2}=\pm \sqrt {14}[/tex]
So, the 4th combination is [tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex]
For [tex]a=5[/tex]
[tex]b=\pm \sqrt {30-5^2}=\pm \sqrt {5}[/tex]
So, the 5th combination is [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex]
The higher integral value of [tex]a[/tex] is not possible for any real [tex]b[/tex].
Hence, the possible combinations of required numbers are
[tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex], [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex], [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex],
[tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex], and [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex].
PLEASE HELP ME FIRST ANSWER GETS BRAINLIST
Answer:
2 its given that cd bisects ab at e so that means e is midpoint of ab
3. vertically opposite angles
4.By SAS congruence
HELP HELP HELP First to HELP gets the brainliest :D
Answer:
[tex]y= -\frac{1}{3}x -6[/tex]
Step-by-step explanation:
Using the slope formula, you can form this equation! The slope of any equation would replace the m, and the y intercept would replace b!
I added in the slope formula at the bottom, just in case, so you'll see what I mean!
I hope this helps, and I explained enough! Have a great day c:
Clare made an error when solving -4x + 3 < 23
-4x + 3 < 23
-4x < 20
x < - 5
Describe the error she made
Help me plzz
Answer:
Clare didn't change the inequality symbol in the last step to >
Step-by-step explanation:
Given inequality is:
[tex]-4x+3<23[/tex]
Clare's error was in the last step where she multiplied the inequality by -4 to remove the minus sign with x. When an in equality is multiplied/Divided by a negative number then the sign of inequality is reversed. < is changed to > and > is changed to less than.
The answer must have been x > -5
The correct way to solve is:
[tex]-4x+3 <23\\-4x<20\\x>-5[/tex]
Hence,
Clare didn't change the inequality symbol in the last step to >
Use the picture below.
How many lines of symmetry does the picture have?
A - 2
B - 3
C - 1
D - 0
(Lol My lil bro asked me and im to lazy for this-)
Answer:
1. I belive
Step-by-step explanation:
If two of the angles in a triangle measure 68 and 23 degrees, what is the measure of the missing angle?
Answer:
89
Step-by-step explanation:
We know that all the inside angles of a triangle summed up is 180 so we just do 68 + 23 which is 91 now we use 180 and subtract 91 from it, 180-91 which equals 89
Which is defined using the undefined terms point and line? angle circle parallel lines ray
Answer:
D. Ray
Step-by-step explanation:
I just finished the quiz!
Point and line segment are used to define a ray.
RayA ray is a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.
A line extends infinitely in either direction but has no width and is one dimensional. A point is a 0-dimensional mathematical object with a location.
Point and line segment are used to define a ray.
Find out more on ray at: https://brainly.com/question/10404182
What is the equation in point-slope form of the line passing through (-2, 0) and (2, 8)?
y = 2(x + 2)
Ob
y = 2(x - 2)
Ос
y = -2(x - 2)
Od
y = -2(x + 2)
Answer:
-8
Step-by-step explanation: y = 2(x +2) so... ( 2x 2) = 4 while 2 - x 2 = 8
Answer:
first one.
Step-by-step explanation:
y=2(x+2).
.....
A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013, the population had reached 236 wolves. Write the equation representing the population N of wolves over time t. Write your answer in the form a(b)^t. Round your b value to 3 decimal places.
Answer:
129 [tex](1.3526)^{t}[/tex]
Step-by-step explanation:
Assuming N = [tex]ab^t[/tex]
t = number of years after 2011
N = number of wolves
When t = 0 , N = 129
129 = [tex]ab^0[/tex]
a = 129
N = 129[tex]b^{t}[/tex]
When t = 2 , N = 236
therefore 236 = 129 [tex]b^{2}[/tex]
[tex]b^{2}[/tex] = [tex]\frac{236}{129}[/tex]
therefore; b = 1.3526
Answer expressed in the form of a(b)^t.
129 [tex](1.3526)^{t}[/tex]
Write an equation in slope-intercept form of the line shown.
Answer:
[tex] y = 2x - 5 [/tex]
Step-by-step explanation:
Find the slope using the points, (1, -3) and (3, 1):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 -(-3)}{3 - 1} = \frac{4}{2} = 2 [/tex]
m = 2
Find the y-intercept (b) by substituting x = 1, y = -3, and m = 2 in [tex] y = mx + b [/tex]
[tex] -3 = (2)(1) + b [/tex]
[tex] -3 = 2 + b [/tex]
Subtract 2 from both sides
[tex] -3 - 2 = 2 + b - 2 [/tex]
[tex] -5 = b [/tex]
[tex] b = -5 [/tex]
Plug in the value of m and b into the slope-intercept form equation, [tex] y = mx + b [/tex].
Thus:
[tex] y = 2x +(-5) [/tex]
✅[tex] y = 2x - 5 [/tex]