The systems of equations which correctly models the situation as described is;
s = 5c ands + c = 48Which systems of equations correctly models the situation as described in the task content?It follows from the task content that the system of equations which models the production process of caffe mocha be determined.
As given in the task content;
Let c represent the number of ounces of coffee.Let s represent the number of ounces of chocolate syrup.Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;
s = 5c.Also, since she wants to make 48 ounces of caffe mocha; we have;
s + c = 48.Therefore, the required system of equations is;
s = 5c ands + c = 48.Read more on system of equations;
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what is 9932.8 rounded to the nearest integer
ANSWER
9933
EXPLANATION
We have the number 9932.8.
We want to round it to the nearest integer.
An integer is a number that can be written without decimal or fraction.
To do that, we follow the following steps:
1. Identify the number after the decimal
2. If the number is greater than or equal to 5, round up to 1 and add to the number before the decimal.
3. If the number is less than 5, round down to 0.
Since the number after the decimal is 8, we therefore have that:
[tex]9932.8\text{ }\approx\text{ 9933}[/tex]Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.C=111.1°a=7.1mb=9.6mOption 1: No triangle satisfies the given conditions.Option 2: c=19.6m, A=26.8°, B=42.1°Option 3: c=16.7m, A=30.8°, B=38.1°Option 4: c=13.8m, A=28.8°, B=40.1°
Answer: Option 4: c=13.8m, A=28.8°, B=40.1°
Explanation:
From the information given,
the known sides are a = 7.1 and b = 9.6
the known angle is C = 111.1
We would find side c by applying the cosine rule which is expressed as
c^2 = a^2 + b^2 - 2abCosC
By substituting the given values into the formula,
c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1
c^2 = 50.41 + 92.16 - 136.32Cos111.1
c^2 = 142.57 - 136.32Cos111.1 = 191.6448
c = √191.6448 = 13.8436
c = 13.8
To find angle A, we would apply the sine rule which is expressed as
a/SinA = c/SinC
Thus,
7.1/SinA = 13.8436/Sin 111.1
By cross multiplying, we have
13.8436SinA = 7.1Sin111.1
SinA = 7.1Sin111.1/13.8436 = 0.4785
Taking the sine inverse of 0.4785,
A = 28.8
Recall, the sum of the angles in a triangle is 180. Thus,
A + B + C = 180
28.8 + B + 111.1 = 180
139.9 + B = 180
B = 180 - 139.9
B = 40.1
Option 4: c=13.8m, A=28.8°, B=40.1°
I need help I already answered just to make sure
The height of the tree is 13.82 m
Step - by - Step Explanation
What to find? Height of the tree.
Given:
• Angle of elevation = 62,°
,• Eye-level above the ground =160cm
,• Distance away from the tree = 6.5m
We need to first sketch the problem, to have a clearer picture of the question.
Change 160cm to meter
160 cm = 160/100 = 1.6 m
Height of the tree = 1.6 + x
We need to find the value of x.
From the sketch above;
Opposite =x
Adjacent =6.5
θ= 62°
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite\text{ }}{\text{adjacent}}[/tex]Substitute the values.
[tex]\tan 62=\frac{x}{6.5}[/tex]Cross-multiply.
x=6.5tan62°
x = 12.22 m
Height of the tree = 1.6 m + 12.22m
Height of the tree = 13.82 m
OR
Height of the tree = 1382 cm approximately.
ranslateSave & Exit CertifyLesson: 10.2 Parabolas11/15Question 9 of 9, Step 1 of 1CorrectFind the equationof the parabola with the following properties. Express your answer in standard form.
Given
[tex]undefined[/tex]Solution
Standard from of a parabola
[tex](x-H-h)^2=4p(y-k)[/tex]Use the strategy to simplify 4/576Write the prime factorization of the radicand.442834O42/2832O 4./283²O4. 2882
To simplify the fraction we will need to facto
In 2009, there were 6.1 million females enrolled in degree granting institutions of higher education. over the next several years this number increased at a rate of 400,000 per year. estimate the number of females enrolled in 2024. y = ______ millionthe equation of the line that models this information is;y = 0.4t + 6.1Determine what year 12.9 million females will be enrolled.
Notice that
400,000 = 0.4 million
That's why the equation that models that information has the factor 0.4, since it expresses the result in millions of females.
Now, we need to notice that t, in the expression 0.4t + 6.1, is the number of years passed since 2009. So, in the year 2024, we have:
t = 2024 - 2009 = 15
Therefore, the number of females enrolled in 2024 can be estimated to be:
y = (0.4 * 15 + 6.1) million
y = (6 + 6.1) million
y = 12.1 million
Now, to determine the year when 12.9 million females will be enrolled, we first need to find t corresponding to y = 12.9, and then add it to the year 2009.
y = 0.4t + 6.1
12.9 = 0.4t + 6.1
12.9 - 6.1 = 0.4t
6.8 = 0.4t
t = 6.8/0.4
t = 68/4
t = 17
Therefore, the year when it happens will be:
2009 + 17 = 2026
Which point is on the circle centered at the origin with a radius of 5 units?Distance formula: Vx2 - xy)2 + (V2 - y2)?(2, 721)(2, 23)(2, 1)O (2,3)
To know if the point is on the circle, we mus calculate the distance between the point and the origin.
For the first option, we have:
- (2, √21)
and the origin
- (0, 0)
Then, we must replace the two points in the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(0-2)^2+(0-\sqrt[]{21})^2} \\ d=\sqrt[]{4+21}=\sqrt[]{25}=5 \end{gathered}[/tex]Knowing that the distancie is 5 we can affirm that the point is on the circle because the radius is 5.
Finally, the answer is
[tex](2,\text{ }\sqrt[]{21})[/tex]White the standard form of the equation of the line through the given point with the given slope.
The standard form equation of a line is expressed as
Ax + By = C
where
A, B and C are real numbers and A and B are not both zero. From the information given,
the line passes through(- 2, 5) and slope = - 4
We would find the y intercept of the line, c by substituting slope, m = - 4, x = - 2 and y = 5 into the slope intercept equation which is expressed as
y = mx + c
Thus, we have
5 = - 4 * - 2 + c
5 = 8 + c
c = 5 - 8 = - 3
Thus, the equation of the line in the slope intercept form is
y = - 4x - 3
We would convert it to standard form. Thus, we have
y + 4x = - 3
4x + y = - 3
Thus, the equation in standard form is
4x + y = - 3
what is 40+56 in GCF
The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
[tex]\begin{gathered} 40=2\cdot2\cdot2\cdot5 \\ 56=2\cdot2\cdot2\cdot7 \end{gathered}[/tex]We now multiply the numbers that appear on both.
[tex]\text{GCF}=2\cdot2\cdot2=8[/tex]We now apply the distributive property:
[tex]8\cdot(5+7)[/tex]For each ordered pair, determine whether it is a solution to 4x - 5y = -13.Is it a solution?x$(x, y)YesNo(-7, -3)(3, -4)OO(-2, 1)oO(6, 7)0
The equation is 4x - 5y = -13.
Substitute -7 for x and -3 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-7)-5\cdot(-3)=-13 \\ -28+15=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation so point (-7,-3) is solution of equation.
Substitute 3 for x and -4 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot3-5\cdot(-4)=-13 \\ 12+20=-13 \\ 32\ne-13 \end{gathered}[/tex]The ordered pair not satisfy the equation. So point (3,-4) is not a solution of the equation.
Substitute -2 for x and 1 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-2)-5\cdot1=-13 \\ -8-5=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation. So point (-2,1) is solution of equation.
Substitute 6 for x and 7 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot6-5\cdot7=-13 \\ 24-35=-13 \\ -11\ne-13 \end{gathered}[/tex]The orderedpair not satisfy the equation. So point (6,7) is not a solution of the equation.
Answer two questions about Equations A and B
A. 2r-1= 5x
B. -1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by combining like terms
Rewrite one side (or both) using the distributive property
In the given equation A, we can (A) subtract the same quantity from both sides.
What are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, obtain equation B from equation A:
Equation A: 2x - 1 = 5xEquation B: -1 = 3xWe can subtract (2x) from both sides to get equation B as follows:
2x - 1 = 5x2x - 2x - 1 = 5x - 2x-1 = 3xTherefore, in the given equation A, we can (A) subtract the same quantity from both sides.
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Translate the sentence into an inequality.Twice the difference of a number and 2 is at least −28.Use the variable x for the unknown number.
To answer this question we have to identify the elements of the inequality.
1. The difference of a number and 2 is represented by the expression: x-2.
2. Twice the difference (...) is represented by the expression: 2(x-2).
3. At least is represented by the sign greater than or equal to ≥.
4. The result is -28.
By putting these all together we obtain the inequality:
[tex]2(x-2)\ge-28[/tex]It means that the answer is 2(x-2) ≥ -28.
Use the formula for n^P_r to evaluate the following expression.
Use the following formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Then, for 11P6:
[tex]\begin{gathered} _{11}P_6=\frac{11!}{(11-6)!}=\frac{11!}{5!}=\frac{5!\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{5!} \\ _{11}P_6=6\cdot7\cdot8\cdot9\cdot10\cdot11=332640 \end{gathered}[/tex]Hence, the result is 332640
Find the probability of getting 4 aces when 5 cards are drawn from an ordinary deck of cards
First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:
(a standard deck card has 52 cards)
[tex]C\left(52,5\right)=\frac{52!}{5!\left(52-5\right)!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48\operatorname{\cdot}47!}{5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}47!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48}{120}=2,598,960[/tex]Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.
Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:
[tex]P=\frac{48}{2598960}=\frac{1}{54145}[/tex]The probability is 1/54145.
Calculate the slope of the given line using either the slope formula m = y 2 − y 1 x 2 − x 1 or by counting r i s e r u n . Simplify your answer. You can choose your method.
The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with the points (-8, 3) and (0,1) we get:
[tex]m=\frac{1-3}{0-_{}(-8)}=\frac{-2}{8}=-\frac{1}{4}[/tex]What do you notice about the measures of the sides or the measures of angles that form triangles?
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
Quadrilateral ABCD is a rhombus.DA АC СBMatch the reasons that justifies the given statements.
A rhombus is a quadrilateral with 4 congruent sides.
For the Rhombus ABCD given
[tex]\begin{gathered} AB\mleft\Vert DC\text{ }\mright? \\ \\ \text{Opposite sides of a rho}mbus\text{ are parallel} \end{gathered}[/tex]Also,
[tex]\begin{gathered} DA\cong CB \\ \text{Opposite sides of a rhombus are congruent} \end{gathered}[/tex]Also,
[tex]\begin{gathered} <\text{ADC}\cong<\text{ABC} \\ \text{Opposite angles of a rhombus are congruent} \end{gathered}[/tex]the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions
You can read a pie chart as follows
Looking at the given pie chart.
The budget for Research is arounf 1/6
The budget for Engineering is around 2/6
The budget for Support is around 1/8
The budget for media and marketing are 1/16 each
The budget for sales is around 3/16
a) The department that has one eight of the budget is Support.
b) The budgets for sales and marketing together add up to
[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]Multiply it by 100 to express it as a percentage
[tex]\frac{1}{4}\cdot100=25[/tex]25% of the budget correpsonds to sales and marketing
c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3
[tex]\frac{18}{3}=6[/tex]The budget for media is 6%
Which parabola corresponds to the quadratic function y = 2x2 + 4x - 16? D. A. B. C. 10:13 1618 10- 12 =10 10 28 -20
We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]The graph that satisfies the conditions we have found previously is the option A.
A linear regression model for the revenue data for a company is R=25.9t + 204 where R is total annual revenue and t is time since 1/31/02 in years.
The linear regression model is
[tex]R=25.9t+204[/tex]Where
R is the total annual revenue (dependant variable)
t is the time, in years, since 1/31/02 (independent variable)
To predict the annual revenue for the period ending 1/31/10, the first step is to determine the value of t. Considering that t=0 is the first recorded year (1/31/02), the value of t corresponding to period 1/31/10 is the number of years passed since, including 2002, which is 9 years.
So you have to calculate R for t=9. Replace the formula with t=9 and calculate the corresponding value of R
[tex]\begin{gathered} R=25.9\cdot9+204 \\ R=437.1 \end{gathered}[/tex]R≈437 billion dollars
O A. 1376 square inchesO B. 672 square inchesO C. 1562 square inchesO D. 936 square inches
The seat back cushion is a cuboid. The surafce area can be calculated below
[tex]\begin{gathered} l=26\text{ inches} \\ h=5\text{ inches} \\ w=18\text{ inches} \\ \text{surface area=2(}lw+wh+hl\text{)} \\ \text{surface area=}2(26\times18+18\times5+5\times26) \\ \text{surface area=}2(468+90+130) \\ \text{surface area=}2\times688 \\ \text{surface area}=1376inches^2 \end{gathered}[/tex]given two circles (all circles are similar) , with circumferences of 30cm and 12cm each, find the ratio of their areas. state answer as fraction.
The circumference of a circle is given by the following formula
[tex]C=2\pi r[/tex]where r represents the radius.
The ratio between two circumferences is equal to the ratio of the radius.
[tex]\frac{C_1}{C_2}=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}[/tex]The area of a circle is given by the following formula
[tex]A=\pi r^2[/tex]Then, the ratio between two circle areas is equal to the square of the ratio of the radius, which is the square of the ratio between the circumferences.
[tex]\frac{A_1}{A_2}=\frac{\pi r_1^2}{\pi r_2^2}=(\frac{r_1}{r_2})^2=(\frac{C_1}{C_2})^2[/tex]Then, applying this relation in our problem, the ratio between the areas is:
[tex]\frac{A_1}{A_2}=(\frac{30}{12})^2=\frac{25}{4}[/tex]The ratio between the areas is 25/4.
what is 3 8/9 + 8 1/2
During Thanksgiving Break, 68% of a school's students ate green bean casserole. Out of 650 students, how many ate green bean casserole?
650 --- total
650*.68=442
442 students ate green bean casserole
.68 represents the percentage
so for example, if they asked me for 50% of 1000
we need to multiply 1000*0.5
if they asked for 60% we will multiply 1000*0.6
Find y if the line through (1, y) and (8, 2) has a slope of 3.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]
Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 3 years?
Answer:
The amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Explanation:
Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;
[tex]\begin{gathered} \text{ Principal P = \$500} \\ \text{rate r = 6\% = 0.06} \\ \text{time t = 3 years} \end{gathered}[/tex]Recall the simple interest formula;
[tex]i=P\times r\times t[/tex]substituting the given values;
[tex]\begin{gathered} i=500\times0.06\times3 \\ i=\text{ \$90} \end{gathered}[/tex]Therefore, the amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]how many pennies are in a dollar
Answer: 100
Step-by-step explanation:
$1 =100 pennies
Find the length of the third side. If necessary, write in simplest radical form. 9 5 Submit Answer Answer:
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with c = 9 and a = 5, we get:
[tex]\begin{gathered} 9^2=5^2+b^2 \\ 81=25+b^2 \\ 81-25=b^2 \\ 56=b^2 \\ \sqrt[]{56}=b \\ \sqrt[]{4\cdot14}=b \\ \sqrt[]{4}\cdot\sqrt[]{14}=b \\ 2\sqrt[]{14}=b \end{gathered}[/tex]A wheel is rotating 600 times per minute. Through how many degrees does a point in the edge of the wheel move in 1/2 seconds.
The wheel is rotating 600 times per minute, find how many times rotate in 1 second:
1 minute = 60 seconds
[tex]600\frac{times}{\min}\cdot\frac{1\min}{60s}=10\frac{times}{s}[/tex]Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:
[tex]\frac{10\frac{times}{s}}{2}=5\text{times}[/tex]Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)
[tex]5\text{times}\cdot\frac{360º}{1\text{time}}=1800º[/tex]Then, a point moves 1800º in 1/2 secondsFind the tangent of the angle whose measure is pi/2....pi divided by 2.
We have the following:
[tex]\begin{gathered} \tan \theta=x \\ \tan \frac{\pi}{2}=x \end{gathered}[/tex]the value of pi / 2 is not defined
