A kite flies in the sky with a thread of 68m and makes an angle theta. If tan theta = 15/8, the the height of the kite above the ground is ?
Answers
Answer:
60 meter
Explanation:
[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]
Given following:
hypotenuse: 68 meter
---
tan(θ) ratio = opposite/adjacent = 15/8
---
To find ratio of hypotenuse (use Pythagoras theorem):
(hypotenuse)² = (adjacent)² + (opposite)²
(h)² = (8)² + (15)²
h² = 289
h = √289 = 17
The height of the kite above ground is the opposite size.
[tex]\sf real \ size = ratio \ size[/tex]
[tex]\sf \dfrac{height \ above \ ground}{hypotenuse} = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf \dfrac{height \ above \ ground}{68} = \dfrac{15}{17}[/tex]
[tex]\sf {height \ above \ ground}= \dfrac{68(15)}{17}[/tex]
[tex]\sf {height \ above \ ground}= 60 \ m[/tex]
Answer:
60 m
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)The given scenario can be modeled as a right triangle (see attached diagram) where:
θ = angle the thread makes with the groundhypotenuse = thread of the kiteside opposite the angle = the height of the kite above the groundAs we have been given the hypotenuse (thread) and the angle θ, and need to find the height (side opposite the angle), we can use the sine trigonometric ratio.
The angle θ has been given as a tan trigonometric ratio.
[tex]\sf \textsf{Therefore, if }\tan \theta=\dfrac{15}{8} \textsf{ then } \cos \theta=\dfrac{8}{17} \textsf{ and } \sin \theta = \dfrac{15}{17}[/tex]
To calculate the height of the kite above the ground, substitute the values into the sine ratio formula and solve for height:
[tex]\implies \sin \theta=\sf \dfrac{height}{thread}[/tex]
[tex]\implies \sf \dfrac{15}{17}=\sf \dfrac{height}{68}[/tex]
[tex]\implies \sf height=\dfrac{15}{17} \cdot 68[/tex]
[tex]\implies \sf height=\dfrac{1020}{17}[/tex]
[tex]\implies \sf height = 60 \:m[/tex]
Therefore, the height of the kite above the ground is 60 m.
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Related Questions
A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers use coupons. 36 times out of 40 these results were considered accurate to within 2.5%. what is the confidence interval?
Answers
The confidence interval comes out to be (0.685,0.735).
Calculating the Confidence Level and Other Terms
The confidence level can be calculated as follows,
z = [tex]\frac{36}{40} * 100%[/tex]%
z = 90 %
The margin error is given as, E= 0.025
The p value in this case is 0.71
Calculating the Confidence Interval
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
Confidence interval can be obtained by using the following formula,
(p-E, p+E) = (0.71-0.025, 0.71+0.025).
Therefore, the confidence interval is (0.685, 0.735).
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The marks price of an article is 4500.after allowing some percent of and levying 10% VAT it is sold at 4400, find the discount percent
Answers
The discount percent for the given transaction is calculated as; 6.11%
What is the percentage Discount?We are given;
Mark Price; M.P = 4500
Now, formula for discount amount is;
Discount amount = %Discount * M.P
Discount amount = x% * 4500 = 45x
Also;
Selling price is;
S.P = M.P - Discount Amount
S.P = 4500 - 45x
VAT = Vat% * S.P
VAT = (10%*4500) - 45x
VAT = 450 - 45x
S.P with VAT = S.P + VAT Amount = 4500 - 45x + 450 - 45x = 4950 - 90x
Thus;
4950 - 90x = 4400
Solving for x gives;
x = 6.11%
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15. Find the coordinates of the circumcenter of triangle ABC With the vertices A(3,-1) B(-3,-11) C(3,-8)
Answers
The coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).
How to determine the coordinates?In order to determine the coordinates of the circumcenter of triangle ABC with the given vertices, let its circumcenter be P(x, y). Thus, PA = PB = PC.
By squaring all sides of triangle ABC, we have:
PA² = PB² = PC²
From PA² = PB², we have:
(x - 3)² + (y - (-1))² = (x - (-3))² + (y - (-11))²
(x - 3)² + (y + 1)² = (x + 3)² + (y + 11)²
x² - 6x + 9 + y² + 2y + 1 = x² + 6x + 9 + y² + 22y + 121
-12x - 20y = 120
-3x - 5y = 30 ..........equation 1.
From PB² = PC², we have:
(x - (-3))² + (y - (-11))² = (x - 3)² + (y - (-8))²
(x + 3)² + (y + 11)² = (x - 3)² + (y + 8)²
x² + 6x + 9 + y² + 22y + 121 = x² - 6x + 9 + y² + 16y + 64
12x + 6y = -57 ..........equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
x = -2.5 and y = -4.5.
Therefore, the coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).
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5. Try It #5
If f(x) is a linear function, with f(2)=-11, and f(4)=-25, find an equation for the function in slope-intercept form.
Answers
The function in slope-intercept form is mathematically given as
f(x)=14x+154
What is an equation for the function in slope-intercept form.?
Parameters
f(2)=-11,
f(4)=-25
Generally, the equation for the slope is mathematically given as
[tex]m=\frac{-25+11}{2-}[/tex]
m=7
In conclusion, the line equation
y-2=7(x-+11)
y as subject
y=14x+154
f(x)=14x+154
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AB ≅ BC and AD ≅ CD
Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
Answers
The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
How to illustrate the information?From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.
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Answer:
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
✔ AC and BD are perpendicular.
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
✔ AX and CX are congruent.
Step-by-step explanation:
right on edge
HELP ASAP!!!
REASONS ONLY
Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus
Answers
The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
What is a Rhombus?A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
What is the above proof?∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.[tex]\overline {DC}[/tex] ≅ [tex]\overline {BC}[/tex] Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.ABCD is a Rhombus Reason = Its sides are all congruent.Learn more about Rhombus at;
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1/8 of passengers of a train were children. if there were 40 children travelling in the train on a certain day, how many adults were there in the train?
Answers
280 adults were there in the train.
What is linear equation definition and example?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of linear equation is y=mx + b. noun. 20. A polynomial equation of the first degree (such as x = 2y - 7)Given,
Total children are in the train = 40
1/8 are children in train and no of children in train ,
∴ 1/8 × x = 40
x = 40 × 8 ⇒ 320
The no of passenger in train = 320
in total passenger, 40 are children .
So, rest adults passengers are = 320 - 40 ⇒ 280
There fore, 280 adults were there in the train.
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Given: 4x + 5 = −6x + 5
Prove: x = 0 using two column proof
Answers
1) [tex]4x+5=-6x+5[/tex] (given)
2) [tex]4x=-6x[/tex] (subtraction property of equality)
3) [tex]10x=0[/tex] (addition property of equality)
4) [tex]x=0[/tex] (division property of equality)
2,307,419 = two million, three hundred seven thousand, four hundred nineteen
Write each number below in word form.
Ex: 1, 750, 064
218,502
384,057
TOUR
4,012,923
one million, seven hundred fifty thousand, sixty-four
two hundred eighteen thousand, five hundred two
Answers
Hello!
The numbers should be written as :
1,750,064
one million, seven hundred fifty thousand, sixty-four
218,502
two hundred eighteen thousand, five hundred two
384,057
three hundred eighty-four thousand, fifty-seven
4,012,923
four million, twelve thousand, nine hundred twenty-three
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ? The population of Town C in 2000 was of the population in 2005. The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Answers
Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005
This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient
Statement 1 and Statement 2 combined:
Let X= the population in 2000
Let Y= the population in 2005
Let Z= the population in 2010
From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y
Multiply both sides by 3 to get [tex]3X=2Y[/tex]
Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]
=>[tex]Y=1.5X[/tex]
As per statement 2, let's first determine the increase in the number of people from 2000 to 2005
If [tex]Y=1.5X[/tex], we know
X= the population in 2000
1.5X= the population in 2005
[tex]1.5X-X=0.5X[/tex]
So, the population increased [tex]0.5X[/tex] from 2000 to 2005
So, from 2005 to 2010, the population increased at least 0.5X
1.5X= the population in 2005
[tex]1.5X+0.5X=2.0X[/tex]
So, the population in 2010 was at least 2.0X
In other words, the population at least doubled from 2000 to 2010
So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
Answers
Answer:
The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation:
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
got it correct on my quiz
Five little girls taken in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 pounds and 114 pounds on a weighing machine. What was the weight of each one of the five little girls if taken separately
Answers
The weight of each one of the five little girls if taken separately is 242.4 lb.
Weight of each girl when taken separatelyThe weight of each girl can be determined from the average weight of the girls.
Weight of each girl = (Total weight) / number of girls
W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5
W = 1,212/5
W = 242.4 lb
Thus, the weight of each one of the five little girls if taken separately is 242.4.
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What is the down payment for this vehicle: $37,850.00 at 7% down
Answers
Answer:
$2,649.50
Step-by-step explanation:
s
−5(−5x+3)−5x+5= -50
Solve for X
Answers
Answer:
x = -2
Step-by-step explanation:
you can fist distribute -5 into the parenthesis
25x - 15 - 5x + 5 = -50
then combine like terms
20x - 10 = -50
add 10 to both sides
20x = -40
lastly divide both sides by 20
x = -2
that is your answer
ΔXYZ was reflected to form ΔLMN.
Triangle X Y Z is reflected to from triangle L M N. Angle Z Y X is 86 degrees and angle Y X Z is 38 degrees. Angle L N M is 56 degrees and angle N M L is 86 degrees.
Which statements are true regarding the diagram? Check all that apply.
ΔXYZ ≅ ΔLMN
∠Y ≅ ∠M
∠X ≅ ∠L
∠Z ≅ ∠L
YZ ≅ ML
XZ ≅ LN
Answers
ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Reflection is a rigid transformation, hence it produces congruent figures with congruent angles.
∠Y + ∠X + ∠Z = 180 (angle in a triangle)
86 + 38 + ∠Z = 180
∠Z = 56°
Also:
∠N + ∠M + ∠L = 180 (angle in a triangle)
86 + 56 + ∠L = 180
∠L = 38°
ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN
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Suppose that the relation H is defined as follows.
H= = {(2, 7), (2, -1), (-8, -2)}
Give the domain and range of H.
Write your answers using set notation.
domain = = 0
range = 0
X
Answers
Answer:
Domain = {-8, 2}Range = {-2, -1, 7}Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
The train will take 1h, then the bus will take and a half hours. i need to allow half an hour to change between them. how long will the whole journey take?
Answers
Total time for whole journey would be 3 hours.
The total trip is divided into three intervals :-
Travelling by trainTravelling by busTime taken to change between themHence to find the total time of the trip we need time taken in each interval and just add them up.
The final expression would be :-
Total time taken = Time taken by bus + Time taken by train +
Time taken to change between them
Given:-
Time taken by bus = 1.5 hrsTime taken by train = 1 hrsTime taken to change between them = 0.5 hrsThus Total time for whole journey would be 3 hours.
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I need help to find the justification for this problem!
Answers
The tangents that exists between the two given circles are not common tangents because they are not of the same size or circumference.
What is a tangent?A tangent can be defined as the plane line that touches a curved surface such as a circle but doesn't pass through the circle.
From the diagram given, the two circles are not of the same size, that is, they have different circumstances. This means that the point where the line meets the both circles are not the same.
Therefore, the tangents that exists between the two given circles are not common tangents.
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Tiger Biscuits factory planing to produce 10,000 units in Month Standard time per 200 units is 8 hours! the Company pays. Rs. 40 per her.
Answers
The total cost or amount that Tiger Biscuits will pay will be Rs 16000.
How to calculate the cost?From the information given, the factory is planing to produce 10,000 units and the standard time per 200 units is 8 hours.
The time taken to produce 10000 units will be:
= (10000/200) × 8
= 400 hours.
The amount that the company will pay will be:
= 400 × Rs 40
= Rs 16000
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help me please im in a rush i need help
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area of shaded region = 34 cm²
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Area of shaded region = Area of bigger rectangle - Area of smaller rectangle.
Area (big) :
[tex] \qquad❖ \: \sf \:13 \times 6[/tex]
[tex] \qquad❖ \: \sf \:78 \: \:c m {}^{2} [/tex]
Area (small) :
[tex] \qquad❖ \: \sf \:11 \times 4[/tex]
[tex] \qquad❖ \: \sf \:44 \: \: cm {}^{2} [/tex]
Area of shaded region :
[tex] \qquad❖ \: \sf \:78 - 44[/tex]
[tex] \qquad❖ \: \sf \:34 \: \: cm {}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Area of shaded region = 34 cm²
The price of a car is £2750.
In a sale, the price is reduced by 20%
Work out the price of the car in the sale
Answers
Answer: $2200
Step-by-step explanation:
20% = 0.2
2750 x 0.2 = 550
2750 - 550 = 2200
OR
2750 x (1-0.2) =
2750 x (0.8) = 2200
Answer:
£2200
Step-by-step explanation:
Formula:
20% off
so:
2750x0.20= x Price of car with 80% off
2750-x= Price of car with 20% off
Find answer:
(look in image to see my work on 2750x0.20, I used Microsoft Whiteboard)
2750x0.20=550.00
2750-550=2200
The price of the car 20% off is £2200
A local business has an area reserved behind the store for a parking lot that is 78 meters long by 19 meters wide. The stalls of the lot are at 90° angles to a required aisle that bisects the lot. The aisle is 8 meters by 78 meters.
An area reserved for a parking lot is 78 meters long by 19 meters wide. 2 stalls and an aisle are in the reserved area. The aisle is 78 meters long and 8 meters wide.
Use the layout of the parking lot to answer the questions.
What is the total area available for cars to park?
m2.
If the parking spaces are compact, they have an area of 12.5 m2. How many compact parking spaces will fit in the lot?
.
If the parking spaces are not compact, they will be 3 meters by 5.5 meters. How many noncompact parking spaces will fit in the lot?
.
Answers
The total area available for cars to park will be 858m².
How to calculate the area?The area of the parking lot will be:
= 78 × 19
= 1482m²
The area of aisle will be:
= 8 × 78
= 624m²
The available area will be:
= 1482m² - 624m²
= 858m².
The compact parking spaces that will fit in the lot will be:
N × 12.5 = 858
N = 858/12.5
N = 68
The non compact parking spaces that will fit in the lot will be:
N × 16.5 = 858
N = 858/16.5
N = 52
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lol please help me goodness gracious
Answers
To find x = [tex]\frac{1}{2} (AB+CD)[/tex]
[tex]x=\frac{1}{2} (46+25)\\\ x=\frac{1}{2} (71)\\ x =35.5[/tex]
Hope it helps!
What is the solution (a, b) to this system of linear equations? 3a 6b=45 2a-2b=-12 (-27, 6) (-1, 7) (1, 7) (27, -6)
Answers
The solution of the system of linear equation are (1, 7)
How to solve system of equation?3a + 6b = 45
2a - 2b = -12
multiply equation(ii) by 3
Therefore,
3a + 6b = 45
6a - 6b = -36
9a = 9
a = 1
Hence,
2(1) - 2b = -12
2 - 2b = -12
-2b = -12 - 2
- 2b = - 14
b = -14 / -2
b = 7
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A student can pitch a fast ball at 65 miles per hour. Convert this
speed to yards per second.
O 95.33 yd/sec
O 132.95 yd/sec
O 31.77 yd/sec
O 21.67 yd/sec
Answers
Answer:
31.77 yd/sec
Step-by-step explanation:
Conversions:
1 mile = 1760 yards1 hour = 3600 secondsGiven:
[tex]\sf 65\:miles\:per\:hour=65\:miles/hour=\dfrac{65\:miles}{hour}[/tex]
Therefore, to convert 65 mph to yards per second:
[tex]\implies \sf \dfrac{65\:miles}{hour}=\dfrac{65 \times 1760\:yards}{3600\:seconds}=31.777...\:yd/s[/tex]
Answer:
c.) 31.77... yd/sec
Explanation:
Given: 1 hours → 65 miles
Conversions:
(i) 1 hour = 60 minutes = 3600 seconds
(ii) 1 miles = 1760 yards
Then,
1 hour = 3600 seconds65 miles = (1760 × 65) = 114400 yards Speed:⇒ distance/speed
⇒ 114400/3600
⇒ 31.77777...
⇒ 31.77 yd/sec
linear slope help pls
Answers
A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the linear table is,
m = ($4,000 - $2,500)/(12-6) = $250 per cars
Hence, the slope of the given linear table is $250 per car.
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Bill's Roast Beef sells 8 times as many sandwiches as Pete's Deli. The difference between their sales is 434 sandwiches. How many sandwiches did each sell?
Answers
Okay, so let's call B = the number of sandwiches Bill sells
and P = the number of sandwiches Pete sells
Since Bill sells 7 times as many sandwiches as Pete, then
B = 7P
And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then
B - P = 434
So, now we can substitute for B from the equation above B = 7P
x = bill's
y = pete's
x = 8y
B - P = 434
7P - P = 434
6P = 434
P = 72.33
Therefore, Pete sells 72.33 sandwiches
Bill sells 7 x 72.33 = 506 sandwiches.
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A recipe calls for 11 tablespoons of sugar and 22 teaspoons of salt. How many
teaspoons of salt are needed for just one tablespoon of sugar?
On the double number line below, fill in the given values, then use multiplication or
division to find the missing value:
Answers
It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.
What are word problems?Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.
From the given information:
If it takes 11 tablespoon + 22 teaspoon to make 1 recipe.i.e.
11 tablespoon of sugar + 22 teaspoon of salt = 1 recipe
Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.
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In a class test containing 20 questions, 5 marks are given for every correct answers, ( -2 ) marks given for every incorrect answers and zero mark for question not attempted. Anju gets 9 correct answer and 11 incorrect answers. What is her total score?
Answers
Answer:
she has 23 points
Step-by-step explanation:
hope this helps and mark brainliest please
help me please!!!! 15 points
Answers
Answer:
17 sq. cm
Step-by-step explanation:
1st you split into 2 smaller shapes
Smaller shape:
A = lw
= 1(2)
= 2
Bigger Shape:
A = lw
= 3(5)
= 15
Add them together
15 + 2 = 17