It is given that,
John has 4 different flags that he wants to hang on the wall.
To find the number of different ways can the flags be arranged in a row:
There are 4! ways can the flags be arranged in a row.
That is,
[tex]\begin{gathered} 4!=4\times3\times2\times1 \\ =24 \end{gathered}[/tex]Hence, the answer is 24 different ways.
Mia was baking cupcakes for a party. She makes four drops of red food coloring for every six drops of yellow food coloring to dye her icing Orange. What is the ratio that would create the same orange color .
To find the ratio that would create the same orange color, we need to find the value from the division of the number of drops of each color of the food coloring.
From the present question, we know that Mia uses 4 drops of red for every 6 drops of yellow. It means that, for every 10 drops, 4 is red and 6 is yellow.
The ratio is:
( I will be finishing once I understand the best way to give you the final answer"
Find the surface area of a parallelogram with adjacent sides u= <4,7, -8> and v= <-2, 5, 11>
Given:
The adjacent sides of parallelogram are u = <4,7,-8> and v = <-2,5,11>
Find:
we have to find the surface area of the parallelogram.
Explanation:
Formula:
Conclusion:
Therefore the surface area of the parallelogram is 125.01.
Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)
a = 65.01, b = 36.38, and c = 42.05.
And it is required to find the measure of angle 0 which will be the angle B
Using the law of cosine
[tex]\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=\frac{a^2+c^2-b^2}{2\cdot a\cdot c}=\frac{65.01^2+42.05^2-36.38^2}{2\cdot65.01\cdot42.05}=0.854 \\ \end{gathered}[/tex][tex]\angle\emptyset=\angle B=\cos ^{-1}0.854=31.31[/tex]the answer is rounded to two decimals
General MathematicsProblem:What interest rate would yield ₱1,200 interest on ₱10,000 in 2 years?
Answer
Interest rate = 6%
Explanation
From the information given in the question,
Interest, I = ₱1,200
Principal, P = ₱10,000
Time, T = 2 years
Interest rate, R = ?
Using Simple Interest formula:
[tex]I=\frac{PRT}{100}[/tex]Since I, P and T are know, we shall substitute these values into the formula to get R.
[tex]\begin{gathered} 1200=\frac{10000\times R\times2}{100} \\ 1200=200R \\ \text{Divide both sides by 200} \\ \frac{1200}{200}=\frac{200R}{200} \\ R=6 \end{gathered}[/tex]Therefore, the interest rate is 6%
Use the protractor to find the measure of ABC. Then classify the angle.
We are asked to find the measure of angle ABC and classify the angle.
As you can see from the figure, vertex A is at 30° and vertex C is at 155°
So, the angle ABC is
[tex]\angle ABC=155\degree-30\degree=125\degree[/tex]So, the angle ABC is 125°
Now recall that an obtuse angle is greater than 90° and less than 180°
Since 125° is between 90° and 180°, therefore, the angle ABC is an obtuse angle.
[tex]m\angle ABC=125\degree,\quad obtuse[/tex]hey, can someone please help me solve this equation? i really need help
Solution
For this case we can use the following definition:
[tex]\cot N=\frac{\cos N}{\sin N}[/tex]And from the figure given we have:
[tex]\cos N=\frac{12}{37},\sin N=\frac{35}{37}[/tex]And replacing we got:
[tex]\cot N=\frac{12}{35}[/tex]Thomas wants to invite Madeline to a party. He has 80% chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's 90% likely to ask her to the party. What is the probability of Thomas inviting Madeline to the party over the phone?
Recall that the probability must add 1, therefore:
[tex]0.6+x=1[/tex]Solving for x, we get:
[tex]\begin{gathered} x=1-0.6 \\ x=0.4 \end{gathered}[/tex]Therefore, the probability of Thomas inviting Madeline to the party over the phone is:
[tex]0.2\cdot0.4=0.08[/tex]or 8%.
Write an inequality to match the statement.The difference of a number x and 7 is less than or equal to the sum of the same number x and 5
The difference of a number x and 7 is less than or equal to the sum of the same number x and 5
The difference means subtraction.
A number is x
Less than or equal is represented with the symbol ≤
So:
The difference of a number x and 7
x-7
is less than or equal to the sum of the same number x and 5
≤ x+5
Altogether:
x-7≤ x+5
Find the slope of the line passing through thepoints (-5,4) and (7,8).
We have two points and we have to calculate the slope of the line pasing through this points.
We can calculate the slope as the ratio of the difference between the y-coordinates and the difference between the x-coordinates.
This can be written as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{7-(-5)}=\frac{4}{7+5}=\frac{4}{12}=\frac{1}{3}[/tex]The slope of the line is 1/3.
A line is drawn over this rectangle . Is the line a line of symmetry?
Answer:
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
Explanation:
A line of symmetry is a line that divides the figure into two equal parts, so when you fold the figure over the line, the two parts will match exactly. So, taking into account the figure, the line drawn is not a line of symmetry.
The answer is
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
Solve for x. -2x+5≤10
Answer:
x≥-2.5
Explanation:
Given the inequality:
[tex]-2x+5\le10[/tex]Step 1: Subtract 5 from both sides of the inequality
[tex]\begin{gathered} -2x+5-5\le10-5 \\ -2x\le5 \end{gathered}[/tex]Step 2: Divide both sides by -2.
Note: Since we divide by a negative number, the inequality sign is reversed.
[tex]\begin{gathered} -\frac{2x}{-2}\ge\frac{5}{-2} \\ x\ge-\frac{5}{2} \\ x\ge-2.5 \end{gathered}[/tex]The solution to the inequality is x≥-2.5.
find the prime factorization ofa) 2205 and b)2525
(a) 2205.
The prime factorization consist in finding prime numbers which multiplication gives the initial number, to find those prime numbers, we divide the number by 2, 3, or 5, depending on the case. Let's do it.
2205 | 5
441 | 3
147 | 3
49 | 7
7 | 7
1
So, the prime factorization is
[tex]2205=5\times3\times3\times7\times7[/tex](b) 2525.
Let's repeat the process as we did with (a).
2525 | 5
505 | 5
101 | 101
1
So, the prime factorization is
[tex]2525=5\times5\times101[/tex]Point Q is shown on the coordinate grid belowWhich statement correctly describes the relationship between the point (-3,2) and point G
The coordinate of Q is (-3,-2)
The relationship between (-3, -2) and (-3, 2)
(x,y) changes into (x,-y) which is the reflection along x axis
The point (-3, 2) is a reflection of point Q across the x-axis
Answer : The point (-3, 2) is a reflection of point Q across the x-axis
Part 1Carson is g year old Haley is 2 yrs younger than Carson. find the sum of their ages in terms of gPart 2Find some of their ages in "g" years time, in terms of g
Part 1
Carson is "g" years old.
Haley is 2 years younger than Carson, you can express her age as "g-2"
To sum their ages you have to add both expressions:
[tex]\begin{gathered} \text{AgeCarson}+\text{AgeHaley} \\ g+(g-2) \end{gathered}[/tex]To simplify the expression, you have to erase the parentheses and add the like terms, i.e., add both "g-terms"
[tex]\begin{gathered} g+g-2 \\ 2g-2 \end{gathered}[/tex]The sum of their ages in terms of g is: Age(g)=2g-2
Part 2
You need to find some of their ages, this means that you have to choose any value for "g" and determine the age of Carson and Haley
For example:
For g=10 years:
Carson's age: g= 10 years-old
Haley's age: g-2=10-2= 8 years-old
The sum of their ages is: 2g-2=(2*10)-2= 20-2= 18 years
For g=15 years:
Carson's age: g= 15 years-old
Haley's age: g-2= 15-2= 13 years-old
The sum of their ages is: 2g-2= (2*15)-2= 30-2= 28 years
f(x)=4x^2-17x + 3What is the value the discriminant F?How many distinct real numbers zeros does F have?
Answer:
• D=249
,• Two real numbers zeros
Explanation:
Given the quadratic function:
[tex]f\mleft(x\mright)=4x^2-17x+3[/tex]a=4, b=-17, c=3
The discriminant is obtained using the formula:
[tex]\begin{gathered} D=b^2-4ac \\ =(-17)^2-4(4)(3) \\ =289-48 \\ =249 \end{gathered}[/tex]Since the discriminant is greater than 0, the equation has 2 real solutions (or zeros).
Note:
• If D<0, the equation has 0 real solutions.
,• If D=0, the equation has 1 real solution.
Matilda covers the interior faces of a kitchen drawer with shelf paper. The height of the drawer is 3/4 its width and the depth front to back is 7/4 its width. if the exact amount of shelf paper needed is 846 square inches what is the depth of the drawer? help me I need help
To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:
A = 846sq in
the area is equal to:
[tex]A=A_b+A_l[/tex]Where:
Ab is the area of the base of the drawer
Al is the area of the laterals of the drawer
The Area of the base is:
[tex]A_b=\frac{7}{4}x\cdot x=\frac{7}{4}x^2[/tex]And the area of the laterals is the sum of the area of every lateral:
[tex]A_l=2\lbrack(\frac{3}{4}x)\cdot(\frac{7}{4}x)\rbrack+2\lbrack(\frac{3}{4}x)\cdot(x)\rbrack[/tex][tex]A_l=\frac{21}{8}x^2+\frac{3}{2}x^2=\frac{33}{8}x^2[/tex]Then:
[tex]846=\frac{7}{4}x^2+\frac{33}{8}x^2[/tex][tex]846=\frac{188}{32}x^2=\frac{47}{8}x^2=5.87x^2[/tex]The we clear the x:
[tex]\frac{846}{5.87}=x^2[/tex][tex]\sqrt[]{144.12}=x[/tex][tex]x=12.004in[/tex]The depth of the drawer is x= 12,004 inchesSimplify: (2a-4)+2(a-5)-3(a+1)
Answer:
a-17 is the answer for this question
Can you please me with the question on the picture
Solution
[tex]\begin{gathered} \text{Total marbles= 6+}5+4_{} \\ \text{Total marbles =15 marbles} \end{gathered}[/tex]6blue marbles
5 red marbles
4 white marbles
Part A
Formula
Not white means it blue or 5 = 11
[tex]P(\text{Blue given not white)}=\frac{P(B\text{ n W)}}{P(W)}=\frac{\frac{6}{15}\times\frac{6}{15}}{\frac{11}{15}}=\frac{6}{15}[/tex]Part B
If you randomly select a letter from the phrase "Ichiro Suzuki is at the top of the lineup," what is theprobability that you select a consonant? (Your answer must be in the form of a reduced fraction.)Submit Question
Given the phrase "Ichiro Suzuki is at the top of the lineup", you can identify that:
- The total number of letters the phrase has is:
[tex]Total=33[/tex]- The number of consonants the phrase has is:
[tex]Consonants=18[/tex]Therefore, you can find the probability that you select a consonant by dividing the number of consonants in the phrase by the total number of letters:
[tex]P=\frac{18}{33}[/tex]You can reduce the fraction by dividing the numerator and the denominator by 3:
[tex]\begin{gathered} P=\frac{18\div3}{33\div3} \\ \\ P=\frac{6}{11} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{6}{11}[/tex]May I please get help with this problem? for I have got it wrong multiple times and still cannot get the correct answer
Answer:
x = 61.9°
Step-by-step explanation:
Let's take a closer look at our triangle:
Since we're on a right triangle, we can say that:
[tex]\sin(x)=\frac{15}{17}[/tex]Solving for x,
[tex]\begin{gathered} \sin(x)=\frac{15}{17}\rightarrow x=\sin^{-1}(\frac{15}{17}) \\ \\ \Rightarrow x=61.9 \end{gathered}[/tex]1277 concert tickets were sold for a total of $16,267. If students paid $11 and nonstudents paid $17, how manystudent tickets were sold?
Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given that 1277 concert tickets were sold, for a total of $16,267, knowing that students paid $11 and non-students paid $17, we have to determine how many students tickets were sold.
Let's start labeling the variables we have. Say x is the number of tickets sold for students, while y is the number of tickets sold for non-students.
The total number of tickets sold can be found by adding how many students and non-students tickets were sold, i.e.
[tex]x+y=1277[/tex]To find the total amount collected, we have to multiply the number of each ticket sold by its respective fee, adding everything as follows:
[tex]11\cdot x+17\cdot y=16267[/tex]With this, we have the following system of equations:
[tex]\begin{cases}x+y=1277 \\ 11x+17y=16267\end{cases}[/tex]We can solve it using the elimination method. It consists in multiplying any of the equations by a factor (usually the easier equation) that when added to the other equation, one of the variables are cancelled out.
In this case, multiply the first equation by a factor of (-11)
[tex]\begin{cases}-11x-11y=-14047 \\ 11x+17y=16267\end{cases}[/tex]Add the two equations
[tex]\begin{gathered} -11x-11y+11x+17y=-14047+16267 \\ 6y=2220 \end{gathered}[/tex]Divide both sides by a factor of 6
[tex]y=370[/tex]Now we plug it back into the first equation in order to solve for x (i. e the number of tickets sold for students)
[tex]\begin{gathered} x+y=1277 \\ x+370=1277 \\ x=1277-370 \\ x=907 \end{gathered}[/tex]This is how many tickets were sold to students.
10. There is a carnival at a local state park. It cost $5 to get in and $1.50 per ride. .Suppose Maya Mapleton has $25 to spend for the day. Which inequality wouldmodel this situation?5+ 1.50x 2 255x + 1.50 s 255 + 1.50x s 2525x + 1.50 s 5
Let:
B = Maya's budget = $25
c = cost of the entrance = $5
a = cost of each ride = $1.50
x = number of rides
T = total money spent
Therefore:
[tex]\begin{gathered} T\le B \\ where_{} \\ T=c+ax \\ so\colon \\ 5+1.5x\le25 \end{gathered}[/tex]experimental and theoretical
Spinning a three:
experimental = 11/50
theoretical = 1/5
Spinning an even number:
experimental = 21/50
theoretical = 2/5
Spinning an odd number:
experimental: 29/50
theoretical: 3/5
Spinning a number less than 5:
experimental: 21/25
theoretical: 4/5
9. A gallon of lemonade calls for 2 scoops of sugar. If you want to make 5 gallons, how much sugar should you put in? (2 pts)
Answer:10
Step-by-step explanation: if you need 2 for 1 gallon multiply it by 5
you have 1 gallon with 2 scoops
2 for 5 gallons gives you 10 scoops total for 5 gallons
Solve the following equation.
(√x -7) (√x -2)= -18
Answer:NO SOLUTION
Step-by-step explanation:
If a woman making $36,000 a year receives a cost-of-living increase of 2.1%, what will her new salary be?
Answer:
Her new salary is $36756
Explanation:
We need to know how much 2.1% of 36000 is, so:
[tex]\begin{gathered} \frac{x}{2.1}=\frac{36000}{100} \\ x=\frac{36000\cdot2.1}{100} \\ x=756 \end{gathered}[/tex]That corresponds to the cost of living increase.
2x + 9 + 3x + x = __x + __Fill in the empty spaces to make this equation have one solution
Answer:
2x + 9 + 3x + x = 7x + 5
Explanation:
The expression on the left side is equal to
2x + 9 + 3x + x
Adding the like terms, we get
(2x + 3x + x) + 9
6x + 9
Then, the given equation is
2x + 9 + 3x + x = __x + __
To make this equation have one solution, the coefficient of x on the right side has to be different from 6, which is the coefficient of 6x + 9.
Therefore, we can fill the empty spaces as
2x + 9 + 3x + x = 7x + 5
Solving this equation, we get:
(2x + 3x + x) + 9 = 7x + 5
6x + 9 = 7x + 5
6x + 9 - 5 = 7x + 5 - 5
6x + 4 = 7x
6x + 4 - 6x = 7x - 6x
4 = x
Therefore, the only solution is x = 4.
The hypotenuse of a right triangle is 1 centimeter longer than the longer leg. The shorter leg is 7 centimeters shorter than the longer leg. Find the length of the shorter leg of the triangle.
Answer:
[tex]\text{Shorter leg= 5cm}[/tex]Step-by-step explanation:
As a first step to go into this problem, we need to make a diagram:
Let x be the measure of the longer leg.
Now, understanding this we can apply the Pythagorean theorem to find x, it is represented by the following equation:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where,} \\ a=\text{longer leg} \\ b=\text{shorter leg} \\ c=\text{hypotenuse } \end{gathered}[/tex]Substituting a,b, and c by the expressions corresponding to its sides:
[tex]\begin{gathered} x^2+(x-7)^2=(x-1)^2 \\ \end{gathered}[/tex]apply square binomials to expand and gather like terms, we get:
[tex]\begin{gathered} x^2+x^2-14x+49=x^2-2x+1 \\ 2x^2-x^2-14x+2x+49-1=0 \\ x^2-12x+48=0 \end{gathered}[/tex]Now, factor the quadratic equation into the form (x+?)(x+?):
[tex]\begin{gathered} (x-4)(x-12)=0 \\ x_1=4 \\ x_2=12 \end{gathered}[/tex]This means, the longer leg could be 4 or 12, but if we subtract 7 to 4, we get a negative measure for the shorter leg, that makes no sense.
Therefore, the long leg is 12 cm.
Hence, if the shorter leg is 7 centimeters shorter than the longer leg:
[tex]\begin{gathered} \text{Shorter leg=12-7} \\ \text{Shorter leg=}5\text{ cm} \end{gathered}[/tex]2Select all values of x that make the inequality -x + 8 >11 true.A-2B-6С-4D1E3F.-3
To solve this problem, we need to know which values of x would make the inequality -x + 8 > 11 true.
To do this, we will need to solve the equation in terms of x, just like how we normally solve for x in any linear equation.
[tex]-x+8>11[/tex]Using the Addition Property of E
14 Find the percent increase or decrease for each of the following values (indicate whether each is an increase or a decrease). a. 4x to x/ b. 0.25m to 0.5m 5 c. + 2p to d.y to 0.687 8 р 15 Consider the following relationships. TI. 1
The percentage increase or decrease is given by
[tex]\frac{final\: \text{amount}-original\: \text{amount}}{original\: \text{amount}}\times100\%[/tex]Let us find the percentage increase or decrease for the given cases.
a) 4x to x
[tex]\begin{gathered} \frac{x-4x}{4x}\times100\% \\ \frac{-3x}{4x}\times100\% \\ -0.75\times100\% \\ -75\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-75%) since it is negative.
b) 0.25m to 0.5m
[tex]\begin{gathered} \frac{0.5m-0.25m}{0.25m}\times100\% \\ \frac{0.25m}{0.25m}\times100\% \\ 1\times100\% \\ 100\% \end{gathered}[/tex]Therefore, it is a percentage increase (100%) since it is positive.
c) 1/2p to 5/8p
[tex]\begin{gathered} \frac{\frac{5}{8}p-\frac{1}{2}p}{\frac{1}{2}p}\times100\% \\ \frac{\frac{1}{8}p}{\frac{1}{2}p}\times100\% \\ \frac{1}{8}\times\frac{2}{1}\times100\% \\ \frac{2}{8}\times100\% \\ \frac{1}{4}\times100\% \\ 25\% \end{gathered}[/tex]Therefore, it is a percentage increase (25%) since it is positive
d) y to 0.68y
[tex]\begin{gathered} \frac{0.68y-y}{0.68y}\times100\% \\ \frac{-0.32y}{0.68y}\times100\% \\ -0.47\times100\% \\ -47\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-47%) since it is negative.
