Magician Anthony has in his magic hat 14 grey, 8 white and 6 black mice. What is
the least number of mice he has to take out of his hat blindfolded to be absolutely
certain that he has got at least one mouse of each colour?
The least number of mice that he has to take out of his hat would be 23.
How to solve for the least number of miceWe have the following details to solve this problem
x = 14
t = 8
u = 6
n1 = x + t + 1
= 14 + 8 + 1 = 23
n2 = t + u + 1
= 8 + 6 + 1 = 15
n3 = x + u + 1
= =14+6+1=21
From here the
max n (n1, n2, n3) = 23, 15, 21
Hence the least number that has to be taken out would be 23.
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whats 3847-27-33+4636
Answer:
8423
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
For Writing the equation of a line in slope-intercept form.
We must know the two points.
To find out the points, we observe in the diagram where the line cuts.
The line passing through the negative x-axis and negative y-axis.
For x-axis, parallel distance from y-axis.
For y-axis, parallel distance from x-axis.
Two Points from the diagram. (-4,0) and (0,-6).
Formula for slope intercept form using points.
y=mx+b
Slope represented as m.
Slope formula m=\(\frac{y_2-y_1}{x_2-x_1}\)
Submit the above two points in the formula.
m=\(\frac{-6-0}{0-(-4)}\)
m=\(\frac{-6}{4}\)
m=\(\frac{-3}{2}\)
Slope m submit in slope intercept form.
\(y=\frac{-3}{2}x+b\\\)
Simplify the above equation
2y=-3x+2b
For find b submit any one point in the above equation.
I choose (-4,0)
Submit the point in simplified equation.
2(0)=-3(-4)+2b
0=12+2b
2b=-12
b=-6
Submit m and b in the slope intercept form.
\(y=\frac{-3}{2}x-6\\\)
Simplify the equation.
2y=-3x-12
Transpose the right hand terms into left side.
3x+2y+12=0
Therefore, The equation of the line in fully simplified slope-intercept form is 3x+2y+12=0.
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Francisco took $20.00 to the mall. He found a DVD he wanted on sale for 18.50. The sales tax rate in his state is 8%. DOe he have enough money to buy the DVD, including tax?
A. No he need an addional $1.48
B. Yes, and he has $0.02 left over.
C. No, he need an additional $13.30.
D. Yes, and he has $1.50 left over.
Subtract -b + 3 from -11b -4 a. 10b+7 b. -12 - 1 c. 10b - 7 d. -10b - 7
Answer:
d. -10b-7
Step-by-step explanation:
Permutation-
Jake's school will have a field trip, Jake will join their Field Trip and they will go to TAAL VOLCANO in TAGAYTAY.
Combination -
2 boxes of red pens and 2 boxes of black pens, one box contains 15 pens, which cost 15 pesos, how many ways to sell the pens
Answer:
Permutation:
The number of ways Jake can join the field trip with his classmates can be represented as a permutation since the order in which they join the field trip matters. Assuming that Jake and his classmates are the only ones who will join the field trip, the number of ways Jake can join the field trip is:
1 * 1 = 1
Therefore, there is only one way for Jake to join the field trip.
Combination:
The number of ways to sell the pens can be represented as a combination since the order in which the pens are sold does not matter.
There are two boxes of red pens and two boxes of black pens, so there are a total of four boxes of pens. Each box contains 15 pens, so there are a total of 60 pens. We can choose the number of red pens we want to sell from the two boxes of red pens, and the number of black pens we want to sell from the two boxes of black pens. The number of ways to choose the number of red and black pens can be calculated using a combination:
Number of ways to sell pens = C(2,1) * C(2,1) = 2 * 2 = 4
Therefore, there are 4 ways to sell the pens.
1. Exercise 4E Write the following scales in the form of 1:n, where n is a whole number. (a) 5 cm represents 4 m (c) 5 cm represents 4 km (d) 4 cm represents 5 km
The scales in the ratio of 1 : n are:
a) 1 : 80
c) 1 : 80000
d) 1 : 100000
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
a)
5 cm and 4 m
1 m = 100 cm
So,
4 m = 4 x 100 cm
4 m = 400 cm
Ratio.
= 5 cm : 4 m
= 5 cm : 400 cm
= 1 : 80
c)
5 cm and 4 km
1 km = 100000 cm
So,
4 km = 400000 cm
Ratio.
= 5 cm : 400000 cm
= 1 : 80000
d)
4 cm and 5 km
1 km = 100000 cm
So,
5 km = 500000 cm
Ratio.
= 5 cm : 500000 cm
= 1 : 100000
Thus,
The scales in the ratio of 1 : n are:
1 : 80
1 : 80000
1 : 100000
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mathmatically indication example with solution
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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Listed below is a table showing the number of employees. 20 years or older by gender in the United states
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
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The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
Barry completed his first semester in college. His grades are in the table below. Using the information: A = 4 points, B = 3 points, C = 2 points, D = 1 point, F = 0 points, calculate Barry's semester grade point average (GPA). Round to the nearest hundredth.
Barry's semester grade point average (GPA). Round to the nearest hundredth is 2.67
How to calculate the GPAThe GPA is calculated by following the procedures
the multiplication
credit hour * grade
= 4 * 3 = 12
= 2 * 4 = 8
= 3 * 2 = 6
= 3 * 2 = 6
sum of the products = 12 + 8 + 6 + 6 = 32
sum of credit hour = 4 + 2 + 3 + 3 = 12
The GPA
= sum of the products / sum of credit hour
= 32 / 12 = 2.67
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A total of 50 randomized samples were assigned into 5 different treatment groups in a pharmaceutical science experiment. Each group includes 10 persons (subjects). In order to test if any difference is discernible among these 5 treatments, one-way ANOVA was conducted for the study. Here are data we calculated: Sum of square between group = 232. Sum of square within group = 400.Subject Treatment 1 Treatment 2 Treatment 3 Treatment 4 Treatment 51 2
---
10ANOVA Summary Table
Source Sum of Square Degree of freedom Mean Square F
Between 232
Within 400
Totala. State null hypothesis and alternative hypothesis. b. Calculate the degree of freedom between group, and the degree of freedom within group. c. Mean squares between groups. d. Mean squares within groups.e. F ratiof. If critical value of F is 2.61, should we reject or accept the null hypothesis?g. State your conclusion for this research.
The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments
How to calculate the valuesDegree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45
Mean squares between groups is calculated as follows:
Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58
Mean squares within groups is calculated as follows:
Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places
F ratio is calculated as follows:
F= Mean squares between groups/Mean squares within groups
= 58/8.89
= 6.524184477
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Determine the domain of which the following function is increasing
Answer:
domain : - ∞ < x < 1
Step-by-step explanation:
the function is increasing on the upward part of the curve. that is
from negative infinity to the vertex at (1, 3 )
domain : - ∞ < x < 1
9. A quilt pattern will use the block shown in the graph with regular hexagon
ABCDEF that has points A(4,0) and D(-4, 0). What is the area of the hexagon
to the nearest tenth? Show all work. [5 points]
From the given coordinates of point A(4, 0), and D (-4, 0), the area of the hexagon is 33.94 units square.
How can the area of the hexagon be found?The given parameters are;
Shape of the quilt pattern = A regular hexagon
Coordinates of point A = A(4, 0)
Coordinates of point D = D(-4, 0)
Required;
The area of the hexagon
Solution;
The coordinates of the center of the hexagon, P = (0, 0)
A regular hexagon consist of six equilateral triangles.
The length of a side of the triangle = PA
Length of PA = 4 - 0 = 4
Therefore;
Length of a side of the triangle = 4
Height of the triangle = PA × sin(60)
Which gives;
Height of the triangle = 4 × (√3)/2 = 2•√3
Area of one triangle = (4 ÷ 2) × 2•√3 = 4•√2
Area of the 6 triangles is therefore;
A = 6 × 4•√2 = 24•√2
Area of the 6 triangles = Area of the hexagon
Therefore;
Area of the hexagon = 24•√2 = 33.94 square units.Learn more about the area of regular shapes here;
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Pls help with this question pls and thx!
The slope of MN¯¯¯¯¯¯¯ is −3.
Which segments are parallel to MN¯¯¯¯¯¯¯?
Select each correct answer.
Responses
WX¯¯¯¯¯¯, where W is at (2, 6) and X is at (4, 0)
segment W X, , where , W, is at , begin ordered pair 2 comma 6 end ordered pair, and , X, is at , begin ordered pair 4 comma 0 end ordered pair
RS¯¯¯¯¯, where R is at (1, 3) and S is at (4, 2)
segment R S, , where , R, is at , begin ordered pair 1 comma 3 end ordered pair, and , S, is at , begin ordered pair 4 comma 2 end ordered pair
TU¯¯¯¯¯, where T is at (8, 1) and U is at (5, 10)
segment T U, , where , T , is at , begin ordered pair 8 comma 1 end ordered pair, and, U, is at , begin ordered pair 5 comma 10 end ordered pair
PQ¯¯¯¯¯, where P is at (5, 6) and Q is at (8, 7)
TU is parallel to MN.
Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.
Therefore,
Considering the line TU, find the slope = y₂-y₁ / x₂-x₁
= 10-1 / 5-8 = -9/3 = -3
Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.
Hence TU is parallel to MN.
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type of car is considered to be
Answer:
non - living thing
Step-by-step explanation:
what the question
Answer:
Um a telsa i guess.
Step-by-step explanation:
Complete the equation to show how to use the distributive property to express the sum of 30 + 45
with a greatest common factor
30 + 45 = ____ ( ____ + ____ )
Answers
15(2 + 3)
5(6 + 9)
75
1,350
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark ( 1 ) for the fraction bar.
Consider that the coordinates of the mid-point of a line segment is given by the formula,
\(\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}\)The given diagram represents the line segment between the points (-3,4) and (-6,-1).
So the corresponding mid-point is given by,
\(\begin{gathered} x=\frac{-3+(-6)}{2}=\frac{-9}{2} \\ y=\frac{4+(-1)}{2}=\frac{3}{2} \end{gathered}\)Thus, the mid-point of the given line segment is ( -9/2 , 3/2 ) .
Wyatt is paying back a loan with a nominal interest rate of 13.62%. If the interest is compounded quarterly, how much greater is Wyatt’s effective interest rate than his nominal interest rate? a. 0.96 percentage points b. 0.40 percentage points c. 0.25 percentage points d. 0.71 percentage points
Answer:
d. 0.71 percentage points
Step-by-step explanation:
13.62 % is .1362 in decimal
quarterly period compounding makes periodic (quarterly) interes rate
= .1362/4 = .03405 per period
FOUR periods in a year
(1+ .03405)^4 = 1.1433
which means effective interest is .1433 or 14.33 %
14.33 - 13.62 = .7115 percentage points difference
A survey of 400 students yielded the following information: 262 were seniors, 215 were commuters, and 150 of the seniors were commuters. How many of the 400 surveyed students were seniors or were commuters?
Out of the 400 surveyed students, 327 were either seniors or commuters.
To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.
According to the information given:
There were 262 seniors.
There were 215 commuters.
150 of the seniors were also commuters.
To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.
Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters
= 262 + 215 - 150
= 327
Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.
It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.
This ensures an accurate count of the students who fall into either category.
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2x+5y=20 y=-0.4x-1 i really need help over here
Answer:
x=6.25 and y=1.5
Step-by-step explanation:
Given equation
2x+5y=20
y=0.4x-1
Putting the value of y in above equation
2x+5(0.4x-1)=20
2x+2x-5=20
4x-5=20
4x=20+5
4x=25
x=6.25
Now,
y=0.4x-1( Given)
Putting the value of x=6.25 in above equation y
y=0.4(6.25)-1
y=2.5-1
y=1.5
In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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Solve for x.
3x + 7 = 28
O A. x=-7
OB. x= 2.3
O c. x=7
OD. = 11.6
E. x = 18
Answer:
The answer is C, x = 7.
Step-by-step explanation:
3x + 7 = 28
-7. -7
3x = 21
/3. /3
x = 7
-2x+2y = -22 7x + 10y = -25
To solve this system of equations we must make the coefficients of y equal in values and different in signs, then multiply equation (1) by -5
\(\begin{gathered} -2x(-5)+2y(-5)=-22(-5) \\ 10x-10y=110(3) \end{gathered}\)Add equations (2), (3) to eliminate y
\(\begin{gathered} (7x+10x)+(10y-10y)=(-25+110) \\ 17x+0=85 \\ 17x=85 \end{gathered}\)Now divide both sides by 17 to find x
\(\begin{gathered} \frac{17x}{17}=\frac{85}{17} \\ x=5 \end{gathered}\)Substitute the value of x in equation (1) to find the value of y
\(\begin{gathered} -2(5)+2y=-22 \\ -10+2y=-22 \end{gathered}\)Add 10 to both sides
\(\begin{gathered} -10+10+2y=-22+10 \\ 0+2y=-12 \\ 2y=-12 \end{gathered}\)Divide both sides by 2 to find the value of y
\(\begin{gathered} \frac{2y}{2}=\frac{-12}{2} \\ y=-6 \end{gathered}\)The solution of the system of equation is (5, -6)
To estimate 179% of 41 by rounding, use the expression
.
Using the distributive property, the expression is equivalent to
.
179% of 41 is about
The estimate of 179% of 41 by rounding is about 73.19.
To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.
Since we are rounding, we round this value to the nearest whole number, which is 73. Therefore, the direct answer is 179% of 41 is about 73.When estimating by rounding, we look at the decimal places. In this case, the hundredth place is 3. Since 3 is less than 5, we round down. Hence, the estimate is 73.19. It is important to note that rounding introduces some degree of error, as the actual value is 73.39. However, for most practical purposes, an estimate provides a close approximation that is quick and easy to calculate.For more similar questions on whole number
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A= -(-9x+10)(4x-3)-(4x-9)
The simplified equation of the function A= -(-9x+10)(4x-3)-(4x-9) is A= 36x² - 17x + 39
How to determine simplify the equation for A in the function?From the question, we have the following equation that can be used in our computation:
A= -(-9x+10)(4x-3)-(4x-9)
To make the equation legible, we need to rewrite it
So, we have the following representation
A= -(-9x + 10)(4x - 3) - (4x - 9)
Next, we expand the brackets
This gives
A= -(-36x² - 27x + 40x - 30) - (4x - 9)
Next, we open the brackets
So, we have the following representation
A= 36x² + 27x - 40x + 30 - 4x + 9
Solving further, we collect the like terms
A= 36x² + 27x - 40x - 4x + 30 + 9
Solving further, we evaluate the like terms
A= 36x² - 17x + 39
Hence, the equation is A= 36x² - 17x + 39
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Given a triangle with legs a and b and hypotenuse c, find the length of side b if c=2b, a=\(\sqrt[2]{3}\)
\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{2}\\ a=\stackrel{adjacent}{\sqrt[2]{3}}\\ \qquad \sqrt{3}\\ b=opposite\\ \end{cases} \\\\\\ 2^2=(\sqrt{3})^2+b^2\implies 4=\sqrt{3^2}+b^2\implies 4 = 3 +b^2 \\\\\\ 1=b^2\implies \sqrt{1}=b\implies 1=b\)
Answer:2
Step-by-step explanation:
yw
the question is 2pX3qX5r
Answer:
Step-by-step explanation:
2p * 3Q * 5r = 30 pqr
You can multiply the integers in any order. When multiplied they always give the same answer no matter what the order.
What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
Answer:its b
Step-by-step explanation:
edge 2020
Answer:its b
Step-by-step explanation:
find by a digit to make the number divisible by 3 1234?
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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