Answer:
3056 can be be formed as the smallest four digit number
A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2
Let's make y the subject of the equation.
[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The correct option is A
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]A school bus with the football team left Jefferson HighSchool and drove at an average speed of 48 mph. A schoolbus with the cheerleading squad left 2 hours later and wasable to catch up to the football team after 6 hours. Whatwas the speed of the bus carrying the school's cheerleadingsquad?
Given data
A school bus with the football team from Jefferson High School drove at an average speed of 48mph
Another school bus with the cheerleading squad left 2 hours later and caught with the football team after 6 hours.
Required
To find the speed of the bus carrying the Cheerleading squad.
Step 1
Determine the distance the bus carrying the football team had travelled in the first 2 hours
Speed is given as
[tex]\begin{gathered} \text{speed =}\frac{dis\tan ce}{time} \\ \text{where sp}eed\text{ = 48mph} \\ \text{time = 2 hours} \\ \text{distance = sp}eed\text{ x time} \\ \text{distance = 48 x 2 =96miles} \end{gathered}[/tex]Step 2
Determine of the distance covered by the bus with the football team in the next 6 hours and find the total distance in 8 hours
[tex]\begin{gathered} \text{Distance = sp}eed\text{ }\times\text{ time} \\ where \\ \text{speed = 48mph} \\ \text{time = 6 hours} \\ \text{Distance = 48 }\times\text{ 6 = 288 miles} \end{gathered}[/tex]The total distance in 8 hours covered by the bus = 288 + 96 = 384miles
Step 3
Determine the speed of the bus carrying the Cheerleaders
The total distance to be covered by the Cheerleaders is 384 miles
The total time of their journey to catch with the bus carrying the Football team is 6hours
Hence the speed of the bus required is given as
[tex]\begin{gathered} \text{Speed = }\frac{dis\tan ce}{time} \\ \text{speed = }\frac{384}{6} \\ \text{speed = 64mph} \end{gathered}[/tex]Therefore, the speed of the bus carrying the school's Cheerleaders squad is 64mph
4. Which inequality is represented by the graph?8642S-6428X4-6laO4x - 2y > 12O4x - 2y < 12O4x + 2y > 12O4x + 2y < 12
Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.
First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:
We can easily find the points (0, -6) and (2, -2).
With this, we can find the equation of the line using the point-slope formula:
[tex]y-y_0=m\cdot(x-x_0)[/tex]Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]Plugging the coordinates of the points, we get:
[tex]m=\frac{-2-(-6)}{2-0}=\frac{-2+6}{2}=\frac{4}{2}=2[/tex]Such that:
[tex]\begin{gathered} y-(-6)=2\cdot(x-0) \\ y+6=2x \end{gathered}[/tex]Rearranging it in the ax + by = c form,
[tex]2x-y=6[/tex]Multiply both sides of the equation by a factor of 2
[tex]4x-2y=12[/tex]Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:
[tex]4x-2y>12[/tex]All the point (x, y) satisfying this inequality are contained in the shaded region.
Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:
Let's check the options
A.
2x - 1 = 2
2x= 3
x= 3/2=1.5
option A has atleast one solution
B
3y+ 1 = 3y
option B has no solution
C.
5p - (3 + p) = 6p + 1
5p - 3 - p = 6p + 1
4p - 6p = 1 + 3
-2p = 4
p =-2
option C has atleast one solution
D.
4/5 m = 1- 1/5 m
4/5 m + 1/5m = 1
1m = 1
m = 1
Option D has atleast one solution
E.
10 + 0.5w = 1/2w - 10
0.5 w - 1/2 w = -10 - 10
option E has no solution
F.
4a + 3(a-2) = 8a - (6+a)
4a +3a - 6 = 8a -6 - a
7a -6 = 7a - 6
option F has many solution. Hence it also has atleast one solution
Therefore;
option A, C, D and F has atleast one solution
what is the answer to a negative 4 divided by a positive 6?
The expression given as negative 4 divided by a positive 6 has a value of -2/3
How to evaluate the expression?From the question, the expression is given as
negative 4 divided by a positive 6
Rewrite the expression properly
This is rewritten as follows
-4 divided by +6
This can be represented as
-4/6
There are no like terms in the above expression
So, we have the following equation
-4/6 = -4/6
Divide 4 and 6 by a common factor
The common factor is 2
So, we have
-4/6 = -2/3
The expression cannot be further simplified
So, we have the following equation
-4/6 = -2/3
Hence, the value of the expression is -2/3
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The expression given as "negative 4 divided by a positive 6" has a value of that is -2/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
From the problem, the expression is given as;
"negative 4 divided by a positive 6"
Rewrite the expression properly then;
-4 divided by +6
This can be express as;
-4/6
There are no like terms in the expression
So, we have the equation;
-4/6 = -4/6
Divide 4 and 6 by a common factor;
The common factor is 2
-4/6 = -2/3
So, we have the equation;
-4/6 = -2/3
Hence, the value of the expression will be; -2/3
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Each n in the model represents the same value. 136.5 What is the value of n? there are 7 N's in the problem
The value of n must be 136.5/7
n = 136.5/7
n = 19.5
Result n = 19.5
A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
see the figure below to better understand the problem
we have that
tan(10∘)=140/x -----> by TOA
solve for x
x=140/tan(10∘)
x=794 ft
therefore
The answer is 794 feetAnswer:
Step-by-step explanation:
tan 10=140/x
x=140 / tan 10
x=794
What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3
The initial expression is:
[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:
[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]So is option C)
2. Given: ZMOP is a right angle RP I OP Prove: MO || RP
Given that;
[tex]\begin{gathered} \measuredangle MOP\text{ is a right angle.} \\ \measuredangle MOP=90^0 \end{gathered}[/tex]And;
[tex]\vec{RP}\perp\vec{OP}[/tex]Since line RP is perpendicular to line OP, Angle RPO must be a right angle.
[tex]\measuredangle RPO=90^0[/tex]Recall that for two parallel lines intersected by a straight line, Same side interior angles are supplementary.
[tex]A+B=180^0[/tex]So, for line MO to be parallel to line RP, the sum of angle MOP and angle RPO must be equal to 180 degree.
[tex]\measuredangle MOP+\measuredangle RPO=90+90=180^0[/tex]Since the sum of angle MOP and angle RPO is equal to 180 degree, then line MO is parallel to line RP.
[tex]\begin{gathered} \text{ Since} \\ \measuredangle MOP+\measuredangle RPO=180^0 \\ \text{Then;} \\ MO\Vert RP \end{gathered}[/tex]Proved
This not a test btw ! But can you please help me with this !
Using elimination:
[tex]\begin{gathered} (A)-3(B)\colon \\ 6x+12x-3y+3y=-4-15 \\ 18x=-19 \end{gathered}[/tex]Therefore, the answer is:
B) Multiply A by 1 and B by -3
Drag the measurements to the containers to show equal length
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]STEP 2: Write the formula for finding sum of arithmetic series
STEP 3: Find the sum of the series
By substitution,
[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]Hence, the sum is 416
ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points
To find:
We need to find two points on the linear equation y-1=0 and to plot those points on graph.
Step by step solution:
We know that:
General coordinate of any two points on line y = 1:
= (x, 1)
So let us assume any two random points on the line:
= (1,1) and (2,1)
We will now mark them on the graph:
Please help and answer this question ASAP! :)
Answer:
Odd, Even, Even, Neither=========================
The difference between odd and even functions is that:
f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.Let's test this property for the given functions.
Function f(x)f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd functionFunction g(x)g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even functionFunction j(x)j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even functionFunction k(x)k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even functionI need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.
we have that
Let
x ------> the distance in miles from a point on the ground (the red line)
In the right triangle of the figure
sin(6.5)=7,000/x
solve for x
x=7,000/sin(6.5)
using a calculator
x=61,835.70 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
61,835.7 ft=61,835.7/5,280=11.71 miles
therefore
the answer is 11.71 miles15% of $764.69rounded to the nearest cent.
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
A reflection across which line(s) carries the trapezoid onto itself?
If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.
Question 17
2(h - 6) + 20 = -4
NEED ASAP ILL GIVE BRAINLIEST IF CORRECT
-10 is no less than 2 times a number plus 14
Let the number be x.
Then according to the question,
[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]Thus, the number should be greater than or equal to -12.
Rob earns $4200 per month at his new job. He pays the following taxes: 6.2% for social security 1.45% for Medicare 16% for federal income tax • 5.5% for state income tax Calculate his annual net income.
Answer:
$35,708.4
Explanation:
His net income will be the total that he earns less the taxes.
So, we need to calculate how much money does Rob pays for each tax.
Therefore, 6.2% of 4200 is equal to:
[tex]4200\times6.2\text{ \% =4200 }\times\frac{6.2}{100}=260.4[/tex]It means that Rob pays $260.4 each month for social security,
In the same way, 1.45% of 4200 is equal to:
[tex]4200\times1.45\text{ \% = 4200}\times\frac{1.45}{100}=60.9[/tex]16% of 4200 is equal to:
[tex]4200\times16\text{ \% = 4200}\times\frac{16}{100}=672[/tex]5.5% of 4200 is equal to:
[tex]4200\times5.5\text{ \% = 4200}\times\frac{5.5}{100}=231[/tex]Now, we can calculate the net income per month as:
$4200 - $260.4 - $60.9 - $672 - $231 = $2975.7
Finally, his annually net income will be the net income per month multiplied by 12 months:
$2975.7 x 12 = $35,708.4
So, the answer is $35,708.4
9. If L 1 equals 120 then what is the measure of its supplement <2=
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
find the solution to the following system by substitution x + y = 20 y = 3x 8
Based on the substitution method, the solution of the system of the equation is x = 3 and y = 17.
Substitution method:
Substitution method is the way of finding the value of any one of the variables from one equation in terms of the other variable.
Given,
Here we have the system of equations
x + y = 20
y = 3x + 8
Now we need to find the solutions for these equation using the substitution method.
From the given details we know that the value of y is defined as 3x + 8.
So, we have to apply these value on the other equation in order to find the value of x,
x + (3x + 8) = 20
4x + 8 = 20
4x = 20 - 8
4x = 12
x = 3
Now apply the value of x into the other equation in order to find the value of y,
y = 3(3) + 8
y = 9 + 8
y = 17
Therefore, the solution of the equation is x = 3 and y = 17.
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Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]which ordered pair is a solution of 6X + 7 < 21
Substitute 2 for x and 1 for in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]\begin{gathered} 6\cdot2+7\cdot1<21 \\ 12+7<21 \\ 19<21 \end{gathered}[/tex]The inequality is trus so point (2,1) satisfy the inequality.
Substitute 4 for x and 1 for y in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]undefined[/tex]Find LM if LN = 137mm.
Exercise 1: What's In2.Mark’s temperature goes 1.5°C higher from the normal body temperature. What is Marks temperature now?A. 38.5°CB. 37.5°CC. 36.5°CD. 36.5C
The normal body temperature of a human is 37°C.
If Mark's temperature goes 1.5°C higher than that temperature, his new temperature will be:
[tex]\Rightarrow37+1.5=38.5°C[/tex]OPTION A is the correct option.
There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
