Answer:
2/3 cups of flour
Explanation:
Lucas recipe needed 5/6 cup of flour.
Sarah's recipe needed 1/6 cup of flour.
The difference
[tex]\begin{gathered} \text{Difference}=\frac{5}{6}-\frac{1}{6} \\ =\frac{4}{6} \\ =\frac{2}{3}\text{ cups} \end{gathered}[/tex]Therefore, Lucas needed 2/3 cups more of flour.
write each measure in radians and express the answer in terms of π4. 315 degrees 5. -450 degrees
The equivalent measure of (315) degrees in radians will be (7π/4) rads.
As per the question statement, we are provided with an angular measure of 315 in the units of degrees,
And we are required to convert the above mentioned angular measure into it's equivalent unit of radians.
To solve this question, first we need to know about the relation between the two units of angular measure, degrees and radians, which goes as,
[180° = (π) rads]
Now using the unitary method and the above conversion reference point, we get,
[180° = (π) rads]
Or, [1° = (π/180) rads],
And, [315° = {(π/180) * 315} rads]
Or, [315° = {π * (315/180)} rads]
Or, 315° = [π * {(5 * 7 * 3 * 3)/(3 * 3 * 4 * 5)} rads]
Or, [315° = {π * (7/4)} rads]
Or, [315° = (7π/4) rads]
To learn more about Degrees and Radians, click on the link below.
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A slide of 4.1 meters long makes an angle of 27 degress with the ground. How high is the top of the slide above the ground? Round to the nearest hundreth meter.
Answer:
1.86 metres
Explanation:
Given the following
Length of the slide = 4.1m (hypotenuse)
Angle of elevation = 27 degrees
Required
Height of the slide above the ground
Using the trigonometry identity
sin theta = opposite/hypotenuse
sin 27 = H/4.1
H = 4.1sin27
H = 4.1(0.4539)
H = 1.86 metres
Hence the height ofthe slide above the pole is 1.86metre to the hundredth meters
a sphere has a diameter of 3.5 inches what's the volume?
Solution
[tex]\begin{gathered} D\text{ = 3.5} \\ r\text{ = }\frac{D}{2}\text{ = }\frac{3.5}{2}\text{ = 1.75} \\ \text{Volume of a sphere = }\frac{4}{3}\times\pi\times r^2 \\ \text{ =}\frac{4}{3}\times\frac{22}{7}\times(1.75)^2^{} \\ \text{ =}\frac{26.95}{21}\text{ =12.83} \end{gathered}[/tex]Final Answer = 12.83
divide the question(4.8x10^9)/(2.0x10^3)
We operate as follows:
[tex]\frac{4.8\cdot10^9}{2.0\cdot10^3}=2400000[/tex][tex]=2.4\cdot10^6[/tex]Question is shown in image below. Answer format is also shown in image.
For |2x-7|>1:
This absolute value inequality results in two inequalities: 2x-7>1 or 2x-7<-1.
Solve these inequalities to find the answer:
[tex]\begin{gathered} 2x-7>1 \\ 2x>1+7 \\ x>\frac{8}{2} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7<-1 \\ 2x<-1+7 \\ x<\frac{6}{2} \\ x<3 \end{gathered}[/tex]It means that the answer is x>4; x<3.
For |2x-7|<1:
This results in one complex inequality: -1<2x-7<1.
Solve it to find the answer:
[tex]\begin{gathered} -1<2x-7<1 \\ -1+7<2x<1+7 \\ 6<2x<8 \\ \frac{6}{2}It means that the answer is 3For |2x-7|=1:From the equation we can conclude that 2x-7=1 or 2x-7=-1.Solve these equations to find the answer:[tex]\begin{gathered} 2x-7=1 \\ 2x=1+7 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7=-1 \\ 2x=-1+7 \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]The answer is x=3; x=4.Sally has 71 peppermints. Bernard has p fewer peppermints than Sally. Write an expression that shows how many peppermints Bernard has.
an expression is:
y = 71 - p
kamFind the area of the shaded sector.Round to the nearest tenth.167°17.8 ydArea = [ ? ]yd?Enter
We know the area of a cirlce is
[tex]A=\pi\cdot r^2[/tex]This is because, in radians, the angle of a whole circle is
[tex]2\pi[/tex]In order to proceed, we'll use the formula
[tex]167\cdot\frac{\pi}{180}\approx2.9147[/tex]Using this new value, we can now compute the area of the shaded region using the formula
[tex]A=\alpha r^2[/tex][tex]\text{Where }\alpha\text{ is the angle that generates the shaded region in radians}[/tex]In this case we have:
[tex]A=2.9147\cdot(17.8)^2=\text{ }923.493548[/tex]Round to the nearest tenth:
[tex]A=923.5yd^2[/tex]The sum of the measures of angle M and angle R is 90°. The measure of angle M is (5x + 10)". The measure of angle R is 55° What is the value of x? Record your answer. Be sure to use the correct place value. B I UE E х, х? KY
Given data:
The given angle M is ∠M=(5x+10)°.
The given angle R is ∠R=55°.
The expression for the sum of both the angles is,
[tex]\angle M+\angle R=90^{\circ}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (5x+10)^{\circ}+55^{\circ}=90^{\circ} \\ 5x=25^{\circ} \\ x=5^{\circ} \end{gathered}[/tex]Thus, the value of x is 5 degrees.
which of the following is equivalent to the expression below? 3(5-2i)A. 15-2iB. 15-6iC. 8-2iD. 8-5i
ANSWER:
B. 15 - 6i
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3\left(5-2i\right)[/tex]We apply the distributive property and we are left with the following:
[tex]\begin{gathered} 3\left(5-2i\right)=3\cdot \:5-3\cdot \:2i \\ \\ 3\left(5-2i\right)=15-6i \end{gathered}[/tex]Therefore, the correct answer is B. 15 - 6i
sadie has ananction figure collection of 200 action figures. She keeps 90 percent of the action figures on her wall. how many action figures does she keep on her wall
we have the following:
[tex]\begin{gathered} n=200\cdot\frac{90}{100} \\ n=180 \end{gathered}[/tex]therefore, 180 action figures keep on her wall
solve for x y and z.
let us find z
[tex]\begin{gathered} \cos 30=\frac{adjacent}{\text{hypotenuse}} \\ \cos 30=\frac{z}{24} \\ z=24\cos 30 \\ z=20.7846096908 \\ z=20.8 \end{gathered}[/tex]let us find x.
[tex]\begin{gathered} \sin 30=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30=\frac{\text{height}}{24} \\ height=24\sin 30 \\ \text{height}=12 \\ \\ \cos 45=\frac{adjacent}{\text{hypotenuse}} \\ \cos 45=\frac{12}{x} \\ x=\frac{12}{\cos 45} \\ x=\frac{12}{0.70710678118} \\ x=16.9705627485 \\ x=17.0 \end{gathered}[/tex]let us find y
[tex]\begin{gathered} \tan 45=\frac{opposite}{\text{adjacent}} \\ \tan 45=\frac{y}{12} \\ y=12\tan 45 \\ y=12.0 \end{gathered}[/tex]What is the slope of the line segment?15129601 2 3 4 50-30-303
Ok, so:
To find the slope of the segment, we have to take two points:
Let's take: A(2,6) and B(1,3).
We calculate the slope as this:
m =( ( y2 - y1 ) / ( x2 - x1 )).
Where A( x1, y1) and B( x2, y2) are the points we took.
Then, m = (3 - 6) / (1-2), this is m = -3/-1, and that's equal to m=3
Find the value of the expression when x is 3.x² + 10x + 25
Given
Expression
[tex]x²+10x+25[/tex]Find
Value of the expression when x = 3
Explanation
Substitute x = 3 in the given expression.
we obtain ,
[tex]\begin{gathered} x²+10x+25 \\ (3)^2+10(3)+25 \\ 9+30+25 \\ 64 \end{gathered}[/tex]Final Answer
Therefore, the value of the expression when x = 3 is 64
Given that sine = 0.87, using sin²0 + cos²0 = 1,
find cose (in Quadrant I). Show all your work for
credit - answer given to three decimal
approximation.
Work Shown:
[tex]\sin^2(\theta)+\cos^2(\theta)=1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = \sqrt{1-\sin^2(\theta)} \ \ \ \text{.... cosine is positive in Q1}\\\\\cos(\theta) = \sqrt{1-(0.87)^2}\\\\\cos(\theta) \approx 0.4930517\\\\\cos(\theta) \approx 0.493\\\\[/tex]
May I please get help with this. For I have tried many times to figure out the right answers
Explanation:
Two figures are congruent if they have the same size and shape. In this case, figure B is greater than figure A, so they are not congruent.
However, Figures C and D are congruent and we can map figure C to D by a rotation of 90 degrees counterclockwise about the origin. For example, the point (2, 3) of figure C becomes point (-3, 2), so the rule is
(x, y) ---> (-y, x) which is the rule for a 90 degrees rotation counterclockwise.
Answers:
Are figure A and B congruent? No
Which transformation maps A to B? None of these
Are figure C and D congruent? Yes
Which transformation maps C to D? Rotate figure C counterclockwise 90 about the origin.
Positive numbers are not closed under subtraction. Give an example below.
A set S is said to be closed under subtraction if:
[tex]\forall a,b\in S,\text{ a-b}\in S\text{ and b-a}\in S[/tex]Since the set given is that of positive numbers, we pick two different positive numbers, say 6 and 9.
[tex]\begin{gathered} \\ 9-6=3\in S \\ 6-9=-3\notin S \end{gathered}[/tex]Since -3 is not a positive number, we can then conclude that the set of positive numbers are
a offers three kinds of meat toppings and 17 * a vegetable topping and how many different ways could you select a meat topping or a vegetable topping
Since this restaurant offers three types of meat toppings and seventeen types of vegetable toppings we can use the fundamental counting principle to determine the number of possible outcomes. This is done below:
[tex]3\cdot(17)=51[/tex]We could select 51 possible combinations of meat and vegetable toppings.
Israel y su amigo fueron al cine y compraron dos entradas de cine a 12.50 cada una también compraron dos bolsas de palomitas de maíz y dos bebidas cada bolsa de pantalones de maíz cuestan 2.25 gastaron un total de 33 en el teatro escribir resolver una ecuación para encontrar el costo de una bebida.Israel and his friend went to the movies and bought two movie tickets at 12.50 each they also bought two bags of popcorn and two drinks each bag of corn pants cost 2.25 spent a total of 33 in the theater write solve an equation to find the cost of a drink.
Let,
x = number of drinks/número de bebidas
y = number of popcorn/número de palomitas de maíz
z = number of tickets/número de entradas
A = price of drinks/precio de las bebidas
B = price of popcorn/precio de las palomitas de maíz
C = price of tickets/precio de las entradas
T = total cost/coste total
We get,
[tex]\text{ T = Ax + By + Cz}[/tex]But,
x, y, z = 2
B = 2.25
C = 12.50
T = 33.00
Conectemos los valores a la fórmula para poder determinar el precio de las bebidas.
[tex]\text{ T = Ax + By + Cz }\rightarrow\text{ 33 = A(2) + (2.25)(2) + (12.50)(2)}[/tex][tex]\text{33 = A(2) + (2.25)(2) + (12.50)(2) }\rightarrow\text{ 33 = 2A + 4.50 + 25.00}[/tex][tex]\text{ 33 = 2A + 29.5 }\rightarrow\text{ 2A = 33 -29.5 }\rightarrow\text{ 2A = 3.50}[/tex][tex]\text{ A = }\frac{3.50}{2}\text{ = 1.75}[/tex]Por tanto, el coste de las bebidas es 1.75.
Find the volume of the cone to the nearest 10th power you use 3.14 for pi. In the second box, take the exponent for the label.
The volume of a cone of radius r and height h is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]The cone in the figure has a radius of r = 2.1 cm and a height of h = 6.2 cm.
Substituting:
[tex]V=\frac{\pi\times\lparen2.1cm)^2\times6.2\text{ cm}}{3}[/tex]Using the value 3.14 for pi and calculating:
V = 28.62 cm 3
You should write 28.62 in the first box and 3 in the second box (for cubic cm)
The line y-5= 9/7(x + 4) is graphed in the coordinate plane. Complete the sentences below describing this process. By inspecting the equation, the graph of the line has a slope of.............
We have a line with equation:
[tex]y-5=\frac{9}{7}(x+4)[/tex]The expression of the line is the slope-point form, that is:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point of the line and m is the slope.
As in this case, m = 9/7, then the slope is 9/7.
By inspecting the equation, the graph of the line has a slope of 9/7.
We also know that (x0,y0) = (-4, 5), that belong to the line.
By inspecting the equation the graph of the line passes through the point (-4, 5).
To find the value of y(3) we replace x with the value 3:
[tex]\begin{gathered} y-5=\frac{9}{7}(3+4)=\frac{9}{7}\cdot7=9 \\ y-5=9 \\ y=9+5 \\ y=14 \end{gathered}[/tex]The value of y(3) is 14. The point is (3, 14).
you pick a card at random and put it back and then pick another card at random what is the probability of picking an even number and then picking a five
STEP - BY - STEP EXPLANATION
What to find?
The probability of picking an even number and then picking a five.
Given:
Step 1
State the probability formula.
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex]Step 2
Identify the even numbers and the all possible outcome.
Even numbers =4, 6
Step 3
Find each of the probability.
Let A be the event of picking an even number and B be the event of picking a 5.
[tex]\begin{gathered} P(A)=\frac{2}{4} \\ \\ P(B)=\frac{1}{4} \end{gathered}[/tex]Step 4
Determine the compound probability.
[tex]\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}\times P(B|A) \\ \\ =\frac{2}{4}\times\frac{1}{4} \\ \\ =\frac{2}{16} \\ \\ =\frac{1}{8} \end{gathered}[/tex]Step 5
Convert to percentage.
[tex]\begin{gathered} Probability=\frac{1}{8}\times\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}[/tex]ANSWER
12.5 %
What transformations to the linear parent function, f(x) = x, give the functiong(x) = 3x - 1? Select all that apply.A. Horizontally stretch by a factor of 3.B. Shift left 1 unit.nC. Vertically stretch by a factor of 3.UD. Shift down 1 unit.SUBMIT
We are given a parent function f(x)= x and asked the transformation process that takes it to g(x)=3x-1
PART 1
If g(x) = 3f (x): For any given input, the output g(x) is three times the output of f(x), so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f(x), so the graph is shrunk horizontally by a factor of 3.
In this case, we can state that the function was first stretched by 3.
PART 2
To move a function up, you add outside the function: f (x) + b is f (x) moved up b units. Moving the function down works the same way; f (x) – b is f (x) moved down b units.
We can also say that the function was shifted downwards by 1
ANSWER: OPTION C AND D
how do you find a vertex in intercept form
Quadratic functions can be written in vertex form, or
[tex]y=a\mleft(x-h\mright)^2+k[/tex]This is especially useful because the vertex of the function is found at the point (h, k).
We can find this form by completing squares, for instance, let y be:
[tex]y=x^2+bx+c[/tex]we can see that this equation is equal to
[tex]y=x^2+2(\frac{b}{2})x+(\frac{b}{2})^2-(\frac{b}{2})^2+c[/tex]because
[tex]2(\frac{b}{2})=b[/tex]and
[tex](\frac{b}{2})^2-(\frac{b}{2})^2=0[/tex]However, in this form, we can see that the first 3 terms are a perfect square, that is
[tex]x^2+2(\frac{b}{2})x+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex]hence,
[tex]\begin{gathered} y=x^2+bx+c \\ y=(x+\frac{b}{2})^2-(\frac{b}{2})^2+c \end{gathered}[/tex]If we define
[tex]\begin{gathered} -(\frac{b}{2})^2+c=k \\ \text{and} \\ h=\frac{b}{2} \end{gathered}[/tex]we have that
[tex]y=(x+h)^2+k[/tex]the constant a arise when you have a leading term different from 1 in x^2.
Alyssa spins a spinner with 10 sections of equal size. Each section is colored either blue, green, orange, or red. Alyssa spins the spinner 80 times
The results of the spins are shown.
Color
Number of Spins 16 8
Blue Green Orange Red
16
40
Move numbers to the table to show how many sections of each color are most likely on the spinner.
Color
Number of Sections
Blue Green Orange Red
2
3
4
5
6
Answer:
Answered below with assumption of numbers
Step-by-step explanation:
Using blue = 16 green = 8 orange = 16 red = 40
40/80 or 1/2 is red 1/2 * 10 = 5 sections
16 / 80 or 1/5 is blue or orange = 1/5 * 10 = 2 each
then the rest are green 8 out of 80 or 1/10 = 1
can you please help with the 2 column proofs. It is not a test/quiz
COnsider the figure,
Two triangles are said to be congruent if all their three sides and three angles are equal.
SInce angle K and N are both right angles, we have,
[tex]<\text{MKL}=<\text{MNL}[/tex]The side ML is the shared side, and hence equal for both the triangles.
SInce LM bisects angle KLN, we have,
[tex]<\text{KML}=<\text{NML}[/tex]Thus, from AAS theorem ( stands for Angle-angle-side), when two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
Hence the triangles are congruent.
Which strategy could you apply to find the distance between any two numbers on the number line? ©MPS
To find the distance between any two numbers on the number line you have to subtract the smallest to the greatest
In the parallelogram below, if < A = 34 °, what is the measure of < D?
Given,
The measure of angle A is 34 degree.
Required
The measure of angle D.
It is given that, ABCD is a parallelogram.
According to the property of parallelogram , the opposite sides of the parallelogram are equal and parallel.
The sum of adjacent interior angle between two parallel line is 180 degree.
So,
[tex]\begin{gathered} \angle A+\angle D=180^{\circ} \\ 34^{\circ}+\angle D=180^{\circ} \\ \angle D=146^{\circ} \end{gathered}[/tex]Hence, the measure of angle D is 146 degree.
Karen runs each lap in 7 minutes. She will run less than 63 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
time for each lap = 7 min
today's time run less than 63 min
n = # laps
Step 02:
1 lap ------- 7 min
n laps ------ 63 min
n laps * 7 min = 1 lap * 63 min
n laps < 63 min * lap / 7 min
n laps < 9 laps
The answer is:
She will run less than 9 laps .
hello I'm confused on this question and need help thank you
Given the data:
36, 14, 18, 18, 34
Let's find the standard deviation of the sample distances.
To find the standard deviation, apply the formula:
[tex]S=\sum_{i\mathop{=}1}^n\sqrt{\frac{(x_i-x_{avg})^2}{n-1}}[/tex]Where:
n = 5
Let's first find the average/,mean:
[tex]\begin{gathered} avg=\frac{36+14+18+18+34}{5} \\ \\ avg=\frac{120}{5} \\ \\ avg=24 \end{gathered}[/tex]The mean of the sample is 24.
Now, to find the standard deviation, we have:
[tex]\begin{gathered} S=\sqrt{\frac{(36-24)^2+(14-24)^2+(18-24)^2+(18-24)^2+(34-24)^2}{5-1}} \\ \\ S=\sqrt{\frac{(12)^2+(-10)^2+(-6)^2+(-6)^2+(10)^2}{4}} \\ \\ S=\sqrt{\frac{144+100+36+36+100}{4}} \\ \\ S=\sqrt{\frac{416}{4}} \\ \\ S=\sqrt{104} \\ \\ S=10.20 \end{gathered}[/tex]Therefore, the standard deviation of the given sample distances is 10.20
ANSWER:
10.20
A fast food restaurant sold 35 burgerswith cheese. If the ratio of burgers soldwith cheese compared to withoutcheese was 7:3, how many burgers didthey sell total?
Answer:
The total number of burgers sold is: 50
Problem Statement
The question tells us a restaurant sold 35 burgers with cheese and also that the ratio of burgers sold with cheese compared to burgers sold without cheese is 7:3.
We are asked to find the total amount of burgers sold; with and without the cheese.
SOLUTION
The question already told us that the ratio of burgers sold with cheese to those without cheese is 7:3. This means that for every 7 burgers with cheese sold, the restaurant also sold 3 burgers without any cheese.
This further implies that out of 10 burgers sold at a time, the restaurant must have sold 7 cheeseburgers and 3 burgers without cheese.
This means that we can say:
[tex]35\text{ burgers represent }\frac{7}{10}\text{ of burgers sold by the restaurant}[/tex]If this is the case, then we can also say that:
[tex]\frac{3}{10}\text{ of the total burgers sold is without cheese}[/tex]Thus, we can write an equation stating that "35 burgers plus 3/10 of the total burgers (B) must be equal to the total number of burgers (B)"
This is done below:
[tex]\begin{gathered} 35+\frac{3}{10}\times B=B \\ 35+\frac{3B}{10}=B \\ \text{Multiply both sides by 10} \\ 350+3B=10B \\ \text{Subctract 3B from both sides} \\ 350+3B-3B=10B-3B \\ 350=7B \\ \text{Divide both sides by 7} \\ \frac{350}{7}=\frac{7B}{7} \\ 50=B \\ \\ \therefore B=50 \end{gathered}[/tex]Final Answer
Thus, the total number of burgers sold is: 50